TV constrained reconstruction could obtain perfect results from incomplete data, and has been applied to reduce metal artifact by assuming that the projection contaminated by metal is missing. In TV constrained reconstruction, the selection of a proper step parameter for TV minimization procedure is a key point. However, this parameter is usually selected empirically, and it is a constant for all pixels in the whole image domain, regardless of the difference of missing projection quantity at different pixels. By analyzing the relationship between the missing projections and pixels position, a Weighted Total Variation (WTV) constrained reconstruction method is proposed to reduce metal artifact in this paper. For WTV constrained method, the parameters are no longer the same, but vary over image domain as the introduced information miss rate. The simulation results show that the proposed method is more effective than current TV constraint to reduce metal artifact. Moreover, WTV constrained method is extended to other incomplete projection problems.