In this paper, the problems of stability for switched positive linear systems (SPLSs) under arbitrary switching are investigated in a continuous-time context. The so-called "copositive polynomial Lyapunov function" (CPLF) giving a generalization of copositive types of Lyapunov function is first proposed, which is formulated in a higher order form of the positive states of the underlying systems. It is illustrated in this paper that some classical types of Lyapunov functions can be seen as special cases of the proposed CPLF. Then, new stability conditions are developed by the new Lyapunov function approach. It is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. A numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques. (C) 2013 Elsevier Ltd. All rights reserved.