In this paper, we propose NNASIM, a fast timing-area accurate event-driven simulator for DNN accelerators. NNASIM is a highly modular, parameterized, and extensible modeling framework for customized DNN accelerators. We build accurate parameterized timing and area models for common models like GEMM, ALU array, and crossbar in the accelerator from RTL-level simulations. These models are fed into the event-driven simulator for fast simulation. NNASIM is integrated with the RISC-V simulator. It guarantees the functional correctness of the accelerator simulation at the instruction level. The experimental results show that our model estimates performance and area of deep neural network accelerators with less than 0.76\\% and 2.83\\% error, respectively, compared to RTL implementations. NNASIM allows architects to model the performance and area of the accelerator at a high level, and thus enables the systematic design space exploration of the customized accelerators.