Acceptance-rejection is a widely used method to generate arbitrarily distributed pseudo-random numbers from uniformly distributed pseudo-random numbers. This paper proposes a method to improve accepting efficiency. The method transforms samples that are discarded in the original method into acceptable ones to improve efficiency. With the improved acceptance-rejection method, an arbitrarily distributed pseudo-random number generator is designed, which uses a linear feedback shift register to produce uniformly distributed pseudo-random numbers, and then uses the improved acceptance-rejection scheme to generate arbitrarily distributed pseudo-random numbers. The design is implemented on FPGA. The experimental results show that the design has high output efficiency and wide applicability.