Experiments were carried out to study the coalescence dynamics of a neutrally buoyant liquid-liquid emulsion subjected to a simple shear flow in a Couette device. The effect of shear rate and dispersed phase holdup were studied. The surfactant stabilized emulsions were prepared in a stirred tank at high shear rates which were applied for long times so as to obtain reproducible equilibrium drop size distributions. Low shear rates were used in the Couette device to prevent drop breakup. Sufficiently large drops and density matching ensured that coalescence due to Brownian motion and creaming was negligible and thus the change in drop size distribution with time was entirely due to shear-induced coalescence. The evolving volume density distributions were measured using optical microscopy and image analysis. A population balance model based on Smoluchowski's result for the rate of shear-induced coalescence and an empirical form for the coalescence efficieney was used to describe the system. Shearing results in stabilization of the emulsion, and the coalescence rate reduces with increasing shear rates. The stabilizing effect due to shearing is greater for higher holdups. The drop size distribution for high values of the holdup becomes bimodal at long times. The coalescence efficiency, back-calculated from experimental data, is independent of drop size for low holdups but is size dependent for higher holdups. This work demonstrates a simple experimental method for evaluating the coalescence efficiency for emulsions with high holdups where theoretical models are not available.