Wavelength Division Multiplexing (WDM) technology provides a wideband communication networks by realizing multiple communication channels with different wavelengths on a single optical fiber. In this technology, each node (wavelength router) has a finite number of transmitters/receivers dealing with different wavelengths, where each wavelength is exclusively used for the communication channel between a specific pair of nodes. Thus, some transmission request may require multiple wavelengths going through several nodes before reaching its destination. As a result, the wavelength assignment to nodes is very important for efficient transmission in WDM-based networks. Among regular wavelength assignment topologies, Bidirectional Manhattan Street Network (BMSN) gives high performance to WDM-based networks. In this paper, we present a two-stage heuristic algorithm for the wavelength assignment in BMSN, called a HIWAS (HIerarchical Wavelength Assignment algorithm for BMSN). The first stage of HIWAS finds an initial wavelength assignment hierarchically, not only to avoid a local minimum as best as possible but also to reduce the time complexity. The second stage improves the wavelength assignment by adopting the simulated annealing. The performance of HIWAS is verified through solving two types of random instances, where HIWAS provides a better solution with a shorter time than the best-known existing algorithm.