Maize-sweet lupine intercrop is the most compatible cropping system in maize-based cropping of northwestern Ethiopia. However, nitrogen and phosphorus requirement was not optimized for the system, which limits its production potential and sustainable intensification. A fertilizer experiment was conducted during the 2017 and 2018 main cropping seasons to determine the yield response of maize to applied nitrogen and phosphorus rates under a maize-lupine intercrop system in northwestern Ethiopia. The experiment was conducted at two districts in a total of four environments. Treatments were consisted of four levels of nitrogen (0, 80, 160, and 240 kg N ha-1) and phosphorus (0, 20, 40, and 60 kg P ha-1) arranged in a factorial Randomized Complete Block Design with three replications. Data on grain yield, plant height, no. of kernels ear-1, ear plant-1, thousand kernel weight of maize, and grain yield of lupine were collected. The response of maize equivalent yield to nitrogen, phosphorus, and their interaction, either for its linearity or quadratic, was detected using a single degree of freedom orthogonal contrast test. Polynomial response function used to compute the optimal level of nitrogen and phosphorus. Results indicated that a quadratic response of maize equivalent yield was observed to applied nitrogen, phosphorus, and their interaction. The highest maize equivalent yield (9135 kg ha-1) was obtained at 159/63 N/P kg ha-1 with a yield advantage of 5724 kg ha-1 relative to the unfertilized (3411 kg ha-1). Economic optimum N/P rates not greatly affected by fertilizer cost fluctuations and ranged from 145 to 150 kg N ha-1 and 58 to 61 kg P ha-1. Therefore, maize growing farmers in South Achefer and Mecha areas of northwestern Ethiopia are recommended to use N rates ranging from 145 to 150 kg N ha-1 and P rates ranging from 58 to 61 kg P ha-1 for maize-sweet lupine intercrop system.