Dynamic range compression (DRC) is an essential function in digital hearing aids, which have stringent power consumption constraints. This work minimized the complexity of the DRC algorithm through adopting functional approximation for those involved nonlinear operations. The tradeoff between computation reduction and approximation error was explored for reducing hardware cost without introducing audible artifact. Moreover, finite wordlength analysis is conducted for the wordlength minimization and further complexity saving. The experimental result shows that our design totally reduces 96% computing complexity of the straightforward implementation without introducing audible difference in the output signals. Compared with other approximation methods, our design also requires lower hardware complexity.