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.