Computing-in-memory utilizing emerging non-volatile devices has become a promising architecture for energy-efficient neural network (NN) applications. However, the non-ideal factors of non-volatile devices and analog circuits may incur severe accuracy loss, which cuts the algorithm and hardware design apart. In this paper, we propose a user-friendly, fast, and accurate simulation framework (CIMUFAS) explores the impact of various non-ideal devices/circuits on algorithm accuracy. The CIMUFAS also provides easy-to-use interfaces to flexibly support user-defined models/parameters for specified devices/circuits. Besides, our CIMUFAS framework achieves reasonable overhead simulation time. This CIMUFAS framework is verified with two real CIM chips with <0.04% accuracy mismatch.