The maximum likelihood estimators (MLEs) for the clock phase offset assuming a two-way message exchange mechanism between the nodes of a wireless sensor network were recently derived assuming Gaussian and exponential network delays. However, the MLE performs poorly in the presence of non-Gaussian or nonexponential network delay distributions. Currently, there is a need to develop clock synchronization algorithms that are robust to the distribution of network delays. This paper proposes a clock offset estimator based on the composite particle filter (CPF) to cope with the possible asymmetries and non-Gaussianity of the network delay distributions. Also, a variant of the CPF approach based on the bootstrap sampling (BS) is shown to exhibit good performance in the presence of reduced number of observations. Computer simulations illustrate that the basic CPF and its BS-based variant present superior performance than MLE under general random network delay distributions such as asymmetric Gaussian, exponential, Gamma, Weibull as well as various mixtures.