A wide variety of molecules have now been detected in the Horsehead nebula photodissocation region (PDR) suggesting that: (i) gas-phase and grain chemistries should both contribute to the formation of organic molecules, and (ii) far-ultraviolet (FUV) photodesorption may explain the release into the gas phase of grain-surface species. In order to tackle these specific problems and more generally in order to better constrain the chemical structure of these types of environments we present a study of the Horsehead nebula gas-grain chemistry. To do so we used the 1D astrochemical gas-grain code Nautilus with an appropriate physical structure computed with the Meudon PDR Code and compared our modeled outcomes with published observations and with previously modeled results when available. The use of a large set of chemical reactions coupled with the time-dependent code Nautilus allows us to reproduce most of the observations well, including those of the first detections in a PDR of the organic molecules HCOOH, CH2CO, CH3CHO and CH3CCH, which were thought to be mostly associated with hot cores. We also provide some abundance predictions for other molecules of interest. Understanding the chemistry behind the detection of these organic molecules is crucial to better constrain the environments these molecules can probe.