A new mesoscale weather prediction model, called QNH, is described. It is characterized by a parameter that multiplies the hydrostatic terms in the vertical equation of motion. Models of this type are referred to generically as “quasi-nonhydrostatic.” The quasi-nonhydrostatic parameter gives the model a character that is essentially nonhydrostatic, but with properties that are theoretically thought to result in smoother, more accurate, and stable predictions. The model is unique in a number of other aspects, such as its treatment of lateral boundary conditions, the use of explicit calculation in the vertical direction, and the use of the bounded derivative theory for initialization. This paper reports on the design and test of the QNH model, which represents the first time the applicability of this type of model has been demonstrated for full-physics, mesoscale weather prediction. The dynamic formulation, discretization, numerical formulation, and physics packages of the model are described. The results of a comprehensive validation of the model are presented. The validation includes barotropic, baroclinic (Eady wave), mountain wave, tropical storm, and sea breeze tests. A simulation of a winter storm (with updated lateral boundary conditions) is presented, which shows that the model has significant skill in forecasting terrain-forced heavy precipitation. It is concluded that the QNH model may be valuable for mesoscale weather prediction.