Data-worth analysis plays an essential role in improving the understanding of the subsurface system, in developing and refining subsurface models, and in supporting rational water resources management. However, data-worth analysis is computationally expensive as it requires quantifying parameter uncertainty, prediction uncertainty, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface simulations using standard Monte Carlo (MC) sampling or advanced surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose efficient Bayesian analysis of data-worth using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce the computational cost with the use of multifidelity approximations. As the data-worth analysis involves a great deal of expectation estimations, the cost savings from MLMC in the assessment can be very outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it to a highly heterogeneous oil reservoir simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the estimation obtained from the standard MC. But compared to the standard MC, the MLMC greatly reduces the computational costs in the uncertainty reduction estimation, with up to 600 days cost savings when one processor is used.