Almost all of the existing solutions of aquifer test analysis assume constant discharge rate boundary conditions. In many actual pumping tests, constant discharge cannot be maintained. This paper presents a general solution for an aquifer test with variable discharge. The exact solution of drawdown distribution around an infinitesimally small diameter well in a uniform, horizontal, extensive, homogeneous, and isotropic confined aquifer is presented when the discharge changes with time during the aquifer test period. A general equation for the type curves resulting from any discharge variability is given, and its application for the exponential changes is presented in detail. A simple straight line procedure is proposed for field applications by considering late time drawdown data. The consideration of constant discharge leads to overestimation of transmissivity but storativity is underestimated. Practical application of the discharge variability is illustrated by a field example.