A variety of soft robots with prospective applications has been developed in recent years. As a key component of a soft robot, the soft actuator plays a critical role and hence must be designed carefully according to application requirements. The soft body may deform in undesired directions if no restraint is endued, due to the isotropy of the pure soft material. For some soft robots such as an inchworm-like biped climbing robot, the actuation direction must be constrained with the appropriate structure design of the soft actuator. This study proposes a pneumatic soft actuator (PSA) to achieve pure in-plane bending motion with anisotropic soft and rigid restraints. The in-plane bending pneumatic soft actuator (2D-PSA) is developed with a composite structure where a metal hinge belt is embedded into the soft material. The design method, material choice, and fabrication process are presented in detail in this paper. Tests are conducted to measure the actuating performance of 2D-PSA in terms of the relationship between the bending angle or force and the input air pressure. Dynamic response is also measured with a laser tracker. Furthermore, a comparative experiment is carried out between the presented 2D-PSA and a general PSA, with results verifying the effectiveness of the presented 2D-PSA. A robot consisting of two serially-connected 2D-PSAs and three pneumatic suckers, which can climb on a flat surface mimicking a snake’s locomotion, is developed as an application demo of the presented 2D-PSA. Its locomotion capability presents the in-plane performance and mobility of 2D-PSA.