One way of investigating how genes affect human traits would be with a genome-wide association study (GWAS). Genetic markers, known as single-nucleotide polymorphism (SNP), are used in GWAS. This raises privacy and security concerns as these genetic markers can be used to identify individuals uniquely. This problem is further exacerbated by a large number of SNPs needed, which produce reliable results at a higher risk of compromising the privacy of participants. We describe a method using homomorphic encryption (HE) to perform GWAS in a secure and private setting. This work is based on a proposed algorithm. Our solution mainly involves homomorphically encrypted matrix operations and suitable approximations that adapts the semi-parallel GWAS algorithm for HE. We leverage the complex space of the CKKS encryption scheme to increase the number of SNPs that can be packed within a ciphertext. We have also developed a cache module that manages ciphertexts, reducing the memory footprint. We have implemented our solution over two HE open source libraries, HEAAN and SEAL. Our best implementation took $24.70$ minutes for a dataset with $245$ samples, over $4$ covariates and $10643$ SNPs. We demonstrate that it is possible to achieve GWAS with homomorphic encryption with suitable approximations.