Private neural network inference has demonstrated great importance in various privacy-critical scenarios. However, the primary challenge remaining in prior works is that the evaluation on encrypted data levies prohibitively high run-time and communication overhead. In this work, we present FastSecNet, an efficient two-party cryptographic framework for private inference in the dealer-based pre-processing setting. Specifically, (1) FastSecNet provides an efficient ReLU protocol for the evalution of non-linear layers, which is built up on a recent advanced cryptographic primitive, function secret sharing (FSS). The core of this construction are an optimized ReLU representation and a customized FSS-based ReLU protocol. (2) For linear layer evaluation, we first propose an efficient PRG-based preprocessing protocol based on the fact that one of the inputs is uniformly random in the offline phase. Then, the online phase only communicates one element and consists of lightweight secret-sharing operations in a ring. Extensive evaluations conducted on 4 real-world datasets and 9 neural network models demonstrate that during the online phase, FastSecNet achieves 14× less runtime and 18× less communication cost compared to the state-of-the-art.