Based on the first-principles electronic-structure method, we study the electronic structures, optical properties, and the structural stabilities of the quaternary sulphides Cu2Zn(Ti, Zr, Hf) S4, which are obtained via substituting Ti, Zr, and Hf elements for Sn elements in Cu2ZnSnS4 (CTZS). It is well known that the photovoltaic efficiency of CZTS(Se) will be improved if the Se atoms partially substitute S atoms in CZTS. Our results show that the valence-band top of CZTSe shifts to lower energy and accesses to the valence-band top of Cu(InGa) Se2 (CIGS). Similar to CZTSe, the valenceband tops of Cu2Zn(Ti, Zr, Hf) S4 also shift to lower energies and access to the top of valence-band of CIGS. The high photovoltaic efficiency requires the smooth changes of the valence-band top and energy gap from the window material and the buffer layer to the light-absorption layer. Thus we predict that the photovoltaic efficiency will be improved if Sn atoms are substituted, even partially, by Ti, Zr, Hf atoms in CZTS, just like Se atoms substituting S atoms in CZTS. To obtain some reliable results, we perform the calculations both of PBE functional and HSE06 functional. The changes of valence-band tops from window materials to the light-absorbed materials are similar for PBE functional and HSE06 functional. The absolute values of the valence-band tops with HSE06 are lower in energies compared with PBE functional and the gaps obtained from HSE06 are larger than the gaps from PBE. We also calculate the optical properties of different light-absorbed materials including CZTiS, CZZrS, CZHfS, CZTS and CIGS, in which we mainly focus on the reflectance of different layers from the vacuum to the light-absorbed materials, from the window layers to the buffer layers and from the buffer layers to the light-absorbed layers. For the window layers we consider the ZnO and TiO2, and for the buffer layer we consider the CdS, In2S3, ZnSe and ZnS, etc. respectively. The high-performance solar cell requires low reflectance between the window layer and the buffer layer, the buffer layer and the light-absorbed layer so as to ensure more light transmit to the light-absorbed layer. Our results of reflectance show that ZnO(TiO2)/In2S3(ZnSe)/PVM are possible multilayer structures, with PVM (photovoltaic materials) =CZTS, CIGS, CZTiS, CZZrS, CZHfS. If we replace CdS buffer layer with other n-type semiconductors, the material of the window layer must be replaced accordingly with new materials to reach the lower reflectance. The structural stability of photovoltaics is an important topic in the application of photovoltaics. Our results show that CZTiS, CZZrS and CZHfS are structure-stable at zero temperature in terms of the calculated elastic properties and phonon vibration spectrum. Based on the elastic constants and Poisson-ratio, similar to CdTe, CIGS and CZTS, the CZTiS, CZZrS and CZHfS are ductile materials suitable to be used as the flexible solar cell. Additionally, we have performed the molecular-dynamics simulations at some finite temperatures (100, 800 and 1200 K respectively), calculated the pair-distribution functions and angle-distribution functions. As comparison, we also perform the corresponding molecular dynamics simulations of CZTS and ZnS. Our results show that the structural stabilities of CZTiS, CZZrS, and CZHfS are close to those of CZTS and ZnS. This means that once CZTiS, CZZrS and CZHfS are obtained experimentally, they will be stable. In summary, the novel photovoltaic materials CZTiS, CZZrS and CZHfS studied in detail in this work are potentially the high-performance photovoltaic materials for the solar cell application in the near future.