A time integration scheme based on the Laplace transform (LT) has been implemented in a baroclinic primitive equation model. The LT scheme provides an attractive alternative to the popular semi-implicit (SI) scheme. Analysis shows that it is more accurate than SI for both linear and nonlinear terms of the equations. Numerical experiments confirm the superior performance of the LT scheme. The algorithmic complexity of the LT scheme is comparable with SI, with just an additional transformation to vertical eigenmodes each time step, and it provides the possibility of improving weather forecasts at comparable computational cost. KEYWORDS filtering, forecast accuracy, Laplace transform, numerical weather prediction, time integration 1 Q J R Meteorol Soc. 2019;145:347-355.wileyonlinelibrary.com/journal/qj