Statistical analysis on genomic data can explore the relationship between gene sequence and phenotype. Particularly, counting the genomic mutation samples and associating with related phenotypes for statistical analysis can annotate the variation sites and help to diagnose genovariation. Expansion of the size of variation sample data helps to increase the accuracy of statistical analysis. It is feasible to securely share data from genomic databases on cloud platforms. In this paper, we design a secure counting query protocol that can securely share genomic data on cloud platforms. Our protocol supports statistical analysis of the genomic data in VCF (Variant Call Format) files by counting query. There are three participants of data owner, cloud platform and query party. Firstly, the genomic data is preprocessed to reduce the data size. Secondly, Paillier homomorphic is used so that genomic data can be securely shared and calculated on cloud platform. Finally, the results which be decrypted is used to implement counting function of the protocol. Experimental results show that the protocol can implement the query counting function after homomorphic encryption. The query time is less than 1 s, which provide a feasible solution to share genomic data securely on cloud platform for statistical analysis.