The ultra-fast speed and massive capacity in 5G networks push huge amounts of data to networks. With network function virtualization, these data will go through multiple service functions (SFs) and big data processing/analysis. As a result, the processing delay from such SFs and data processing/analysis can significantly impact the delivery of latency-sensitive services. To reduce the processing delay, network function parallelism techniques are introduced to allow multiple SFs running parallelly for the same request. In this work, we study how to apply network function parallelism into SF chaining and embedding to optimize the latency. When physical nodes have unlimited computing resource, we propose the mixed integer programming based parallelism-aware SFC optimization (MIP-PS) algorithm. Our analysis proves the proposed MIP-PS is integer-approximation. When physical nodes have limited computing resource, we propose the latency factor based parallelism-aware SFC optimization (LF-PS) algorithm. Our extensive simulations demonstrate that our proposed schemes outperform the approaches extended directly from the existing work.