Acoustic camera is a new generation 2D forward-looking imaging sonar, which can generate clear images with high resolution even in turbid water. A fundamental problem to be solved is to determine the camera pose from given 3D points in the world coordinate and corresponding 2D points in the acoustic image. This problem is difficult to be solved analytically with a closed-form solution due to the unique projection theory. Specifically, this study discusses about estimation of camera pose from coplanar points which is a basic problem for camera calibration or resection based on plane targets. To solve this problem, a linearized projection model is used, which is similar to the weak-perspective model for the optical camera, to acquire a closed-form solution for acoustic camera pose. For more precise results, an iterative algorithm can be followed by using the closed-form solution as an initial guess. The proposed method can be applied to pose estimation of the acoustic camera based on targets such as 2D fiducial markers.