A new variational functional for space-time neutronics is presented. This functional is stationary about the integro-differential form of the diffusion equation, in which the delayed neutron source is expressed as a convolution integral of the flux, and an integro-differential adjoint flux equation. The new functional is used to derive a quasi-static method that is similar to the improved quasistatic (IQS) method, except that the equation for the flux shape uses a different expression for the delayed neutron source. In a one-dimensional sub-prompt critical test problem, the new variational quasi-static method was slightly more accurate than the IQS method.