We propose an integrating sphere photometer with six detection ports for total luminous flux measurement, which significantly improves the uniformity of spatial response compared to the conventional single-port detection design. Numerical simulations based on the geometric radiative transfer equation show that a spatial response distribution function of the new design is uniform within 2% with respect to all spatial directions. The related spatial mismatch error is calculated to be less than 0.3% for all the realistic cases of angular intensity distribution of a test lamp. As a result, the new design practically eliminates the spatial mismatch error of an integrating sphere photometer, so that a high-accuracy measurement can be achieved without the complicated spatial mismatch correction procedure.