In this paper, a temporal-asymmetric fractional Langevin-like ratchet is constructed for the operation of a 1D linear molecular motor subjected to both spatial-symmetric periodic potential and temporal-asymmetric unbiased Langevin-like noise. In this ratchet, the Langevin-like noise is used to simulate the intracellular fluctuation induced by ATP hydrolysis. Then, for numerical study of this ratchet, the corresponding discrete mapping is derivated. Finally, as an example, the unidirectional transport of the ratchet driven by unbiased Langevin-like noise, generated by the Logistic mapping, is numerically studied. Negative transport of the ratchet indicates that without the spatial asymmetry of potential, the temporal asymmetry is enough for the presence of unidirectional transport. Since temporal asymmetry has to be regarded as a generic property of nonequilibrium system, this ratchet is expected to be resonably used for the operation of molecular motor.