In this paper, an adaptively constrained stochastic model predictive control (MPC) is proposed to achieve less-conservative coordination between energy storage units and uncertain renewable energy sources (RESs) in a microgrid (MG). Besides the economic objective of MG operation, the limits of state-of-charge (SOC) and discharging/charging power of the energy storage unit are formulated as chance constraints when accommodating uncertainties of RESs, considering mild violations of these constraints are allowed during long-term operation, and a closed-loop online update strategy is performed to adaptively tighten or relax constraints according to the actual deviation probability of violation level from the desired one as well as the current change rate of deviation probability. Numerical studies show that the proposed adaptively constrained stochastic MPC for MG optimal operation is much less conservative compared with the scenario optimization based robust MPC, and also presents a better convergence performance to the desired constraint violation level than other online update strategies.