A symmetric matrix C is completely positive(CP)if there exists an entrywise nonnegative matrix B such that C = B B^T.The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix(i.e.,a matrix having unknown entries)such that the completed matrix is completely positive.We propose a semidefinite algorithm for solving general CP-completion problems and study its properties.When all of the diagonal entries are given,the algorithm can give a certificate if a partial matrix is not CP-completable,and it almost always gives a CP-completion if it is CP-completable.When diagonal entries are partially given,similar properties hold.Computational experiments are also presented to show how CP-completion problems can be solved.