Genetic drive systems have the potential to modify entire insect populations in a few years through the super-Mendelian inheritance of a genetic trait. We describe a novel gene drive system called CRISPRh, which acts as a selfish genetic element in the malaria mosquito Anopheles gambiae. CRISPRh is a synthetic allele containing CRISPR/Cas9 endonuclease designed to specifically target and insert a copy of itself into its homologous chromosome in the germline of heterozygous individuals. Using a gene targeting approach, we identified three genes that confer recessive female sterility upon disruption. By inserting CRISPRh at each of these genes, we achieved super-Mendelian inheritance of CRISPRh alleles, ranging from 91 to 99.6% of the progeny of heterozygotes. Population modelling predicts that these high rates of transmission and a recessive knockout phenotype would enable CRISPRh alleles to spread rapidly through a wild mosquito population, causing population suppression through the generation of sterile females. We tested the potential of one CRISPRh allele to invade a caged population of naïve mosquitoes and observed an average increase from 50-76.4% over six generations, demonstrating the first gene drive designed to spread through a natural vector population. The CRISPRh constructs described here generate strong unintended fertility effects and are highly susceptible to target site resistance, making them unsuitable for malaria control. We expect that simple modifications can solve these issues and allow the development of gene drives for the suppression of mosquito populations to levels that do not support malaria transmission.