PathSim is a widely used meta-path-based similarity in heterogeneous information networks. Numerous applications rely on the computation of PathSim, including similarity search and clustering. Computing PathSim scores on large graphs is computationally challenging due to its high time and storage complexity. In this paper, we propose to transform the problem of approximating the ground truth PathSim scores into a learning problem. We design an encoder-decoder based framework, NeuPath, where the algorithmic structure of PathSim is considered. Specifically, the encoder module identifies Top T optimized path instances, which can approximate the ground truth PathSim, and maps each path instance to an embedding vector. The decoder transforms each embedding vector into a scalar respectively, which identifies the similarity score. We perform extensive experiments on two real-world datasets in different domains, ACM and IMDB. Our results demonstrate that NeuPath performs better than state-of-the-art baselines in the PathSim approximation task and similarity search task.