The most efficient previously proposed oblivious transfer schemes require t calls of 1-out-n oblivious transfer (OT) to construct the t-out-n OT. Its computational requirements and bandwidth consumption are quite demanding. Therefore, to guarantee the quality of growing popular communication service, an efficient t-out-n OT scheme with low bandwidth is urgently desired. Based on elliptic curve cryptosystems, we propose a new t-out-n OT scheme in this paper. Compared with existing OT schemes based on modular exponentiations, our scheme can reduce many computation and communication loads for both the sender and the receiver. Owing to its smaller bandwidth and faster computation speed, our scheme is very suitable for mobile clients and smart-card users. Moreover, our scheme provides a simple algorithm and fewer parameter requirements.