Maize/soybean relay intercropping system (MSR) is a popular cultivation method to obtain high yields of both crops with reduced inputs. However, in MSR, the effects of different strip widths on competitive strengths and grain yields of intercrop species are still unclear. Therefore, in a two-year field experiment, soybean was relay-intercropped with maize in three different strip-width arrangements (narrow-strips, 180 cm; medium-strips, 200 cm; and wide-strips, 220 cm), and all intercropping results were compared with sole maize (SM) and sole soybean (SS). Results showed that the optimum strip-width for obtaining high grain yields of maize and soybean was 200 cm (medium-strips), which improved the competitive-ability of soybean by maintaining the competitive-ability of maize in MSR. On average, maize and soybean produced 98% and 77% of SM and SS yield, respectively, in medium-strips. The improved grain yields of intercrop species in medium-strips increased the total grain yield of MSR by 15% and land equivalent ratio by 22%, which enhanced the net-income of medium-strips (by 99%, from 620 US $ ha−1 in wide-strips to 1233 US $ ha−1 in medium-strips). Overall, these findings imply that following the optimum strip-width in MSR, i. e., strip-width of 200 cm, grain yields, and competitive interactions of intercrop species can be improved.