The α-function method is a family of second-order explicit methods with controlled numerical dissipation. Thus, it is very promising for the pseudodynamic testing of a system where high frequency responses are of no interest. This is because that favorable numerical dissipation can suppress the spurious growth of high frequency responses, which might arise from numerical and/or experimental errors during a test. Furthermore, the implementation of an explicit method for the pseudodynamic testing is much simpler than for an implicit method. The superiority of using this method in performing a pseudodynamic test was verified both analytically and experimentally. In fact, results of error propagation analysis reveal that the spurious growth of high frequency responses can be suppressed and less error propagation is identified when compared to the Newmark explicit method. Actual tests were conducted pseudodynamically to confirm all the analytical results. It is also illustrated that although the high frequency response is insignificant to the total response it may be significantly amplified and propagated and finally destroys the pseudodynamic test results.