Metasurface is a momentous periodic or aperiodic microstructure which has capabilities in controlling polarization of electromagnetic waves. To realize polarization controlling, many microstructures have been designed to achieve the function. However, multi-band linear to dual-circular polarization converter is rarely proposed and designed in the last few years. Here, a quad-band dual-circular transmissive metasurface (QCT-MS) is proposed to manipulate polarization of transmissive wave. QCT-MS is designed as a three-layer microstructure, with substrate in the middle and two metal patches in the shape of bi-symmetrical arrow on both sides. The proposed microstructure manipulates linear polarization waves to dual-circular polarization waves in different frequency bands with x-polarized or y-polarized incident waves. The experimental and simulated results reveal that left-hand circularly polarized waves can be realized in 3.14-3.32, 4.41-4.46, and 14.82-16.05 GHz while the right-hand circularly polarized waves can be achieved from 9.45 to 10.12 GHz for QCT-MS with x-polarized incidences. Moreover, the simulated results also demonstrate its characteristics of wide-angle transmission and periodic changes. The proposed transmissive metasurface can be utilized in multiband communication and multifunctional dual-circularly polarized antenna systems.