Summary: Given a covariance matrix, principal component analysis (PCA) with sparsity constraints considers the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination. However, when loading an input variable is associated with an individual cost, we need to incorporate weights, which represent the loading cost of input variables, into the sparsity constraint. We present a version of PCA with weighted sparsity constraints. This problem is reduced to solving some semidefinite programming ones via a convex relaxation technique. Two applications of the PCA with weighted sparsity constraints to refine the sparsity constraints of sparse PCAs illustrate its efficiency and reliability in practice.