Abstract: In this paper, the conditions guaranteeing the existence of constrained facets in conforming Voronoi tessellation(CVT) in 3D are derived. An algorithm is presented to build a Voronoi tessellation conforming to a piecewise linear complex (PLC) in 3D. To build CVT, a set of balls are constructed covering the 0- and 1-dimension faces of PLC, then Voronoi sites aligned alongside 2D faces of PLC are generated by the conforming regular triangulation of 2D faces of PLC. The algorithm has been implemented to validate its efficiency. It is to our knowledge, the first practical algorithm devoted to solving this problem.