The problem of blind phase offset recovery of low density parity-check (LDPC)-coded systems is considered in this paper. We propose a new algorithm of phase offset estimation that involves the computation and maximization of a likelihood difference (LD)-based cost function calculated from the parity-check matrix of the code. We show in this paper that the new cost function has a simplified form compared to another algorithm proposed in the literature and presents similar estimation performance. Mean squared error (MSE) curves show very good performance of the proposed phase offset estimation algorithm, even at low signal-to-noise ratios.