The problem of L1-induced performance analysis for continuous positive systems with time-delay is investigated in this paper. At first, we propose a integral method to compute the value of the system L1-induced norm, and the relationship between the transfer function and L1-induced norm of such systems is obtained. Then, the necessary and sufficient condition is given to ensure that such systems are asymptotically stable and have a prescribed L1-induced performance by linear Lyapunov function. At last, we get a conclusion that time-delay is independent of the L1-induced performance of such systems.