The Internet of Things (IoT) is an emerging network paradigm that aims to obtain the interactions among pervasive things through heterogeneous networks. Security is an important task in the IoT. Luo et al. (Secur Commun Netw 7(10): 1560-1569, 2014) proposed a certificateless online/offline signcryption (COOSC) scheme for the IoT (hereafter called LTX). Unfortunately, Shi et al. showed that LTX is not secure. An adversary can easily obtain the private key of a user by a ciphertext. Recently, Li et al. proposed a new COOSC scheme (hereafter called LZZ). However, both LTX and LZZ need a point multiplication operation in the online phase, which is not suitable for resource-constrained devices. To overcome this weakness, we propose a new COOSC scheme and prove its security in the random oracle model. In addition, we analyze the performance of our scheme and show its application in the IoT.