This paper investigates asymmetric hardening behavior of the magnesium alloy sheet of AZ31B at different strain rates when deformation is large. Tensile tests are carried out at the quasi-static state of 0.001 s(-1) and the intermediate strain rate of 100 s(-1) utilizing the Instron 5583 and the high speed material testing machine (HSMTM), respectively. Compression tests are conducted at the strain rate of 0.001 s(-1) and 100 s(-1) using a jig fixture mounted on the testing machines to change the loading direction into the opposite direction. A compression testing method is developed to obtain compressive properties with large strain, which includes the attachment of a fork-type clamping device and the design of specimen dimensions to achieve large strain without buckling during the test. Experimental results reveal the asymmetric behavior showing that the tensile yield stress is much larger than the compressive one at both strain rates. The difference between the flow stress level in tension and compression becomes larger when the strain rate is higher. The compressive hardening behavior is very much different from the tensile hardening behavior showing that the compressive flow stress increases remarkably as the deformation proceeds while the tensile flow stress asymptotes to a certain value.