A new fuzzy weighted average computation algorithm (NFWA) based on the α-cuts representation of fuzzy numbers is presented in this paper. For each α-cuts, the endpoints of the fuzzy weighted average (FWA) can be calculated from two particular switch points. In the proposed algorithm, these two switch points are computed with an opposite direction searching process, although recursive, which is remarkably efficient. The calculation complexity of the new algorithm is O(n). Experimental result demonstrates that compared with some commonly used FWA algorithms, the new algorithm approach requires the least CPU time, and then may be the fastest available FWA algorithm to date.