Corn (Zea mays L.)–soybean (Glycine max (L.) Merr.) intercropping is one of the main traditional intercropping systems used. We hypothesized that sweet corn–soybean intercropping with reduced nitrogen application could improve the crops’ fresh grain yield and nitrogen acquisition. We clarified whether sweet corn intercropped with soybean has the advantages of improved crop yield and carbon and nitrogen accumulation and assessed interspecific competition in the intercropping systems. A four-year (2017–2020) field experiment was conducted with three nitrogen application levels (0, 150, and 300 kg∙ha−1) and three planting patterns (monocropped sweet corn, monocropped soybean, sweet corn–soybean intercropping) at Jiangxi Agricultural University, Nanchang, China. The LER (land equivalent ratio), AG (aggressivity), and CR (competitive ratio) were calculated using the fresh grain yield and nitrogen and carbon accumulation of sweet corn and soybean. The LER values were greater than 1.0 in most of the intercropped patterns, except for the value based on the crops’ fresh grain yield without nitrogen application in 2020. Sweet corn had greater values of CR and AG than soybean in the intercropping system. Compared with common nitrogen application (300 kg∙ha−1), reduced nitrogen application (150 kg∙ha−1) did not significantly reduce the LER or the average CR and AG values. Under reduced nitrogen application, the values of LER, CR, and AG, based on the crops’ fresh grain yield and nitrogen acquisition, were not significantly different between the four years. In conclusion, based on the LER, CR, and AG, sweet corn–soybean intercropping had the advantage of crop yield and nitrogen acquisition, and sweet corn was the superior competitor. Sweet corn–soybean intercropping with nitrogen application (150 kg N ha−1) showed good inter-annual stability of crop productivity and competitiveness of the sweet corn.