In the artificial neural networks, tanh (hyperbolic tangent) and sigmoid functions are widely used as activation functions. Past methods to compute them may have shortcomings such as low precision or inflexible architecture that is difficult to expand, so we propose a CORDIC-based architecture to implement sigmoid and tanh functions, which has adjustable precision and flexible scalability. It just needs shift-add-or-subtract operations to compute high-accuracy results and is easy to expand the input range through scaling the negative iterations of CORDIC without changing the original architecture. We adopt the control variable method to explore the accuracy distribution through software simulation. A specific case (ARCH.(1,15,18), RMSE: 10^{-6}) is designed and synthesized under the TSMC 40nm CMOS technology, the report shows that it has the area of 36512.78 um^2 and power of 12.35mW at the frequency of 1GHz. The maximum work frequency can reach 1.5GHz, which is better than the state-of-the-art methods.