We present a new data assimilation algorithm known as the Continuous Data Assimilation (CDA) algorithm that has been tested extensively in the mathematical literature and, most recently, in a downscaling simulation in the atmospheric literature. Unlike more common data assimilation methods, the CDA algorithm has an exponential convergence rate and is computationally efficient. This work is the first attempt to demonstrate the viability of the data assimilation algorithm in large-scale ocean models. We implement the CDA algorithm in the Model for Prediction Across Scales - Ocean in an idealized mesoscale eddy test case, demonstrating the ability of the data assimilation algorithm to capture the net effects of unresolved processes in low-resolution models.