Composability is a key component to improve programmers' productivity in writing fast market-expanding applications such as parallel machine learning algorithms and big data analytics. These applications exhibit both regular and irregular compute patterns, and are often combined with other functions or libraries to compose a larger program. However, composable parallel processing has taken a back seat in many existing parallel programming libraries, making it difficult to achieve modularity in large-scale parallel programs. In this paper, we introduce a new parallel task programming library using composable tasking graphs. Our library efficiently supports task parallelism together with an intuitive task graph construction and flexible execution API set to enable reusable and composable task dependency graphs. Developers can quickly compose a large parallel program from small and modular parallel building blocks, and easily deploy the program on a multicore machine. We have evaluated our library on real-world applications. Experimental results showed our library can achieve comparable performance to Intel Threading Building Blocks with less coding effort.