A chiral metamaterial composed of bilayer twisted split-ring resonators is proposed and demonstrated to realize tunable, dual-directional, and multifunctional polarization conversion for terahertz waves. Simulations show that the converter can selectively achieve linear-to-linear, linear-to-right-handed circular, or linear-to-left-handed circular polarization conversion by tuning the polarization and propagating direction of the incident waves. Stokes parameters, ellipticity, and a polarization rotation angle are introduced to determine the output polarization. The circular polarization transmission coefficients and surface current distribution are employed to demonstrate the physical mechanisms of the phenomena above. The proposed converter can find potential applications in terahertz imaging and communications.