This paper considers time synchronization in wireless sensor networks. When the communication delay is negligible, the maximum time synchronization (MTS) protocol is proposed by which the skew and offset of each node can be synchronized simultaneously. For a more practical case where the intercommunication delays between each connected node are positive random variables, we propose the weighted maximum time synchronization (WMTS), which is able to counteract the impact of random communication delays. Despite the clock offset that cannot be synchronized, WMTS can synchronize the clock skew completely in expectation and achieve acceptable synchronization accuracy. For both protocols, we provide rigorous proofs of global convergence as well as the upper bounds of their convergence time. Compared with existing consensus-based synchronization protocols, the main advantages of our protocols include: 1) a faster convergence speed so that the synchronization can be achieved in a finite time for MTS, and in a finite time in expectation for WMTS, respectively; 2) simultaneous synchronization of both skews and offsets; and 3) random communication delays can be handled effectively. Numerical examples are presented to demonstrate the effectiveness of the proposed protocols.