You can make sure first that the primers used are specific to the gene of interest and there are some online tools which design your primer perfectly. Since you are getting multiple bands so you might wanna try to increase your anealing temperature and secondly you can use a high fidelity polymerase which have a good proofreading activity and also try using less primer concentrations.
You should tell us your PCR conditions so that we can comment more on it.
as mentioned BLAST your primers to verify just one hit to your gene of interest. Regarding increasing the annealing temp to render your PCR more stringent and eliminate non specific bands increase in 1C intervals from Tm-3c to Tm+2C