Necessary and sufficient conditions are derived, using the method of moments, for controllability of a class of distributed parameter systems. Using these conditions a test for controllability of such systems is developed. The test involves checking whether a set of linearly independent elements form a basis for the Hilbert space in which the evolution equation of the distributed system under consideration is described. The test is illustrated by an example. A control-theoretic interpretation is given to the method of moments scheme for solving evolution equations of the type considered.