a symmetric matrix a is completely positive (cp) if there exists an entrywise nonnegative matrix b such that $a = bb^t$. we characterize the interior of the cp cone. we formulate the problem as linear optimizations with cones of moments. a semidefinite algorithm is proposed for checking interiors of the cp cone, and its properties are studied. a cp-decomposition of a matrix in dickinson's form can be obtained if it is an interior of the cp cone. some computational experiments are also presented.