In this paper, we consider the recently proposed hybrid metric-Palatini gravitational theory, which consists of adding to the Einstein-Hilbert Lagrangian an f(ℜ) term constructed à la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we explore the cosmological evolution of a specific model, given by f(ℜ)∝ℜ², and obtain constraints on the free parameters by using different sources of cosmological data. The viability of the model is analyzed by combining the conditions imposed by the supernovae Ia and baryonic acoustic oscillation data and the results are compared with the local constraints.