Given a row-finite k-graph ? with no sources we investigate the K-theory of the higher rank graph C*-algebra, C*(?). When k=2 we are able to give explicit formulae to calculate the K-groups of C*(?). The K-groups of C*(?) for k>2 can be calculated under certain circumstances and we consider the case k=3. We prove that for arbitrary k, the torsion-free rank of K0(C*(?)) and K1(C*(?)) are equal when C*(?) is unital, and for k=2 we determine the position of the class of the unit of C*(?) in K0(C*(?)).