Robust robotic grasping in clutter still remains a challenging problem despite its great practical value. This article presents an information-theoretic exploration approach that aims to improve the grasp estimation quality in a complex environment. First, a lightweight grasp detector that is composed of inverted residual blocks and a pyramid pooling module is proposed to make more accurate pixelwise predictions in real time, which are then projected to the workspace. To measure the uncertainty of estimations in the workspace, a two-dimensional grasp entropy (2D-GE) is defined, and the Gaussian process is applied to regress the variation of the information gain that is approximated by 2D-GEs. Finally, guided by the information gain, depth cost, and distance cost, our approach is able to actively collect and fuse estimations from multiple informative viewpoints through the exploration that finally converges to a refined best grasp, resulting improved grasping performance with a higher success rate and environmental adaptability in clutter. Simulation and robotic experiment are both performed to demonstrate the effectiveness of our method and compare it to baselines.