GC-biased gene conversion (gBGC) is a recombination-associated evolutionary process that biases the segregation ratio of AT:GC polymorphisms in the gametes of heterozygotes, in favour of GC alleles. This process is the major determinant of variation in base composition across the human genome and can be the cause of a substantial burden of GC deleterious alleles. While the importance of GC-biased gene conversion in molecular evolution is increasingly recognised, the reasons for its existence and its variation between species remain largely unknown. Using simulations and semi-analytical approximations, we investigated the evolution of gBGC as a quantitative trait evolving by mutation, drift and natural selection. We show that in a finite population where most mutations are deleterious, gBGC is under weak stabilising selection around a positive value that mainly depends on the intensity of the mutation bias and on the intensity of selective constraints exerted on the genome. Importantly, the levels of gBGC that evolve by natural selection do not minimize the load in the population, and even increase it substantially in regions of high recombination rate. Therefore, despite reducing the population's fitness, levels of gBGC that are currently observed in humans could in fact have been (weakly) positively selected.