In this paper, a novel facet clustering based method is proposed to generate alternative build orientations for laser powder bed fusion. This method consists of two steps. First, a hierarchical clustering algorithm is applied to divide facets of the design model in standard tessellation language format into different clusters, each of which shares a similar normal vector. Second, alternatives of each cluster are computed and the final set of alternative build orientations is generated by combining and refining the alternatives from all clusters. To illustrate and validate the method, a set of examples including both regular and freeform surface models are tested, and qualitative and quantitative comparisons between the method and the existing methods are reported. The results suggest that the proposed method is feasible and effective for both regular and freeform surface parts. It is evident that the proposed method can output stable results, provide satisfying efficiency, and work well with facet clusters of varying probability density.