Sex‐biased gene expression, particularly sex‐biased expression in the gonad, has been linked to rates of protein sequence evolution (nonsynonymous to synonymous substitutions, dN/dS) in animals. However, in insects, sex‐biased expression studies remain centred on a few holometabolous species. Moreover, other major tissue types such as the brain remain underexplored. Here, we studied sex‐biased gene expression and protein evolution in a hemimetabolous insect, the cricket Gryllus bimaculatus. We generated novel male and female RNA‐seq data for two sexual tissue types, the gonad and somatic reproductive system, and for two core components of the nervous system, the brain and ventral nerve cord. From a genome‐wide analysis, we report several core findings. Firstly, testis‐biased genes had accelerated evolution, as compared to ovary‐biased and unbiased genes, which was associated with positive selection events. Secondly, although sex‐biased brain genes were much less common than for the gonad, they exhibited a striking tendency for rapid protein sequence evolution, an effect that was stronger for the female than male brain. Further, some sex‐biased brain genes were linked to sexual functions and mating behaviours, which we suggest may have accelerated their evolution via sexual selection. Thirdly, a tendency for narrow cross‐tissue expression breadth, suggesting low pleiotropy, was observed for sex‐biased brain genes, suggesting relaxed purifying selection, which we speculate may allow enhanced freedom to evolve adaptive protein functional changes. The findings of rapid evolution of testis‐biased genes and male and female‐biased brain genes are discussed with respect to pleiotropy, positive selection and the mating biology of this cricket.