This paper studies the oblique impact of droplets on microstructured superhydrophobic surfaces with the lattice Boltzmann method. Three-dimensional simulations are performed based on the pseudopotential multiphase model, with the Carnahan-Starling equation of state and the multiple-relaxation-time collision operator adopted to overcome the numerical instability problems at high liquid/gas density ratio and low fluid viscosity. The droplet impact dynamics is simulated in a wide range of normal Weber numbers (0-30), Ohnesorge numbers (0.002-3), and impact angles (15 degrees-90 degrees), with particular interest in understanding different types of bouncing behavior and their effects on the contact time. The results show that, among the four possible types of bouncing identified in the simulation, including conventional retracting bouncing, incomplete-retracting bouncing, impaled retracting bouncing, and tumbling bouncing, incomplete-retracting bouncing and tumbling bouncing have less contact time and could be facilitated by increasing the impact obliqueness. The increase in the normal Weber number leads to a transition from conventional retracting bouncing, to incomplete-retracting bouncing, and then to impaled retracting bouncing. The contact time shows a non-monotonic trend of "decrease"-"increase"-"decrease" with enlarged Ohnesorge number, and the sheer drop in the contact time at high Ohnesorge numbers is due to the occurrence of tumbling bouncing. (C) 2018 Elsevier Ltd. All rights reserved.