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The monocular visual-inertial odometry (VIO) based on the direct method can leverage all available pixels in the image to simultaneously estimate the camera motion and reconstruct the denser map of the scene in real time. However, the direct method is sensitive to photometric changes, which can be compensated by introducing geometric information in the environment. In this paper, we propose a monocular direct sparse visual-inertial odometry, which exploits the planar regularities (PVI-DSO). Our system detects the planar regularities from the 3D mesh built on the estimated map points. To improve the pose estimation accuracy with the geometric information, a tightly coupled coplanar constraint expression is used to express photometric error in the direct method. Additionally, to improve the optimization efficiency, we elaborately derive the analytical Jacobian of the linearization form for the coplanar constraint. Finally, the inertial measurement error, coplanar point photometric error, non-coplanar photometric error, and prior error are added into the optimizer, which simultaneously improves the pose estimation accuracy and mesh itself. We verified the performance of the whole system on simulation and real-world datasets. Extensive experiments have demonstrated that our system outperforms the state-of-the-art counterparts.