A new Honeycomb PneuNets (HPN) soft gripper and its grasp strategy are proposed. The theoretical model of the soft gripper has infinite degrees of freedom, so it can fit the surface of the objects completely. In order to calculate the final grasp state, the grasp process is simulated at every selected grasp point according to the characteristics of motion and grasp. For every final grasp state, the decision point is taken to get the feasible solution set using the relative form closure theory. For each feasible solution, the evaluation function for the HPN soft gripper is calculated. Then the best solution is selected to get the best grasp plan. The experimental results show that the new soft gripper and its grasp strategy can greatly improve the grasp success rate on common geometrical objects.