In this paper we present a novel algorithm for identifying continuous-time autoregressive moving average models utilizing irregularly sampled data. The proposed algorithm is based on the expectation-maximization algorithm and obtains maximum-likelihood estimates. The proposed algorithm shows a fast convergence rate, good robustness to initial values, and desirable estimation accuracy. Comparisons are made with other algorithms in the literature via numerical examples. (C) 2016 Elsevier Ltd. All rights reserved.