A single screen terahertz frequency selective surface (FS) using the improved split ring resonators (SRRs) is designed in this paper. The resonance unit of an improved SRR consists of an open seam metal patch, while the physical size of the open seam metal patch will directly affect the stepped impedance characteristics. In the paper, LC equivalent circuit model for the improved SRR unit structure is established to extract the equivalent circuit model parameters. Then the relationship between the fundamental frequency of the FSS formula and the harmonics is obtained from the basic theory of the transmission line. Compared to the traditional uniform SRR, the control of multi-band in the improved SRR is more flexible. It is an outstanding characteristic for multi-band FSS design. Based on this characteristic, the triple-band terahertz FSS centered at 0.46, 0.86 and 1.03 THz respectively is designed successively, which can be used in radio astronomy application. By using HFSS 13.0 electromagnetic software simulation, many important indicators such as the key parameters that affect the transmission characteristics of the FSS, periodic intervals, miniaturization degree and the sensitivity of the incidence angle have been studied and analyzed. Both the theoretical analysis and simulated results demonstrate the validity of the method. The triple-band FSS using the improved SRR has a lot of reformative performances. It is shown that the reflection coefficients of triple-band FSS using the improved SRR are -37.6 dB, -13 dB, and -19.6 dB, respectively. On the other hand, it owns the stable frequency response characteristics in the 0°–60° range, which is beneficial to a large incidence angle. In addition, a high degree of miniaturization and the low loss characteristics are the another two significant advantages of this FSS. This triple-band FSS with improved SRR has potential applications in the terahertz frequency radio astronomy polarizer, beam splitter, mirror and resonator mirror, etc.