Interspecific interactions in intercropping can affect the yield of component crops, but little attention has been given to the dynamics of interspecific competition based on biomass accumulation in various management practices. A field experiment with wheat (Triticum aestivum L.)–maize (Zea mays L.) intercropping was conducted to evaluate the interspecific competition with four types of straw management for wheat (no-tillage with straw standing or mulched soil and conventional tillage with straw incorporation or no straw retained) and two methods of plastic mulching for maize (no-tillage with residual plastic mulching [i.e., new at the beginning of the previous crop, old plastic mulched in season] and conventional tillage with annual new plastic mulching). Aboveground biomass of intercrops was sampled throughout the growing season and fit to a logistic growth model. Compared with sole-cropping, intercropping significantly increased maximum biomass and maximum growth rate of wheat but suppressed vegetative and maximum growth rates of maize. Maize growth recovered after wheat was harvested when maize was blister kernel stage (R2). Straw mulching in wheat strips and residual plastic mulching in maize strips produced greater maximum biomass amount or rates of wheat and maize than that with conventional intercropping (conventional tillage with no straw retention in wheat strips and annual new plastic mulching in maize strips). Straw mulching in wheat strips and residual plastic mulching in maize strips enhanced total grain yields by 14.9% compared with conventional intercropping. Straw mulching in wheat strips and residual plastic mulch in maize strips are suitable for coordinating interspecies interactions and increasing the productivity of wheat–maize intercropping.