We employ the four-component relativistic extended-coupled-cluster (ECC) method to compute the permanent electric dipole moment (PDM) of a few open-shell diatomic molecules in their ground electronic state. The computed results are compared with the available results obtained from the experiments and two other coupled-cluster-based methods− Z-vector technique and linear expectation-value approach within the relativistic framework. The study reveals that the relativistic ECC method accurately predicts the PDM of the molecules under consideration and also are in good agreement with these two aforementioned correlated methods.