Concerning the problem that current genetic comparison protocols generally require a trusted third party, which may result in the leakage of a wide range of private data, a genetic comparison scheme based on linear scan was proposed. The gene sequences of two parties were first encoded based on Garbled Circuit (GC), and then the genome database was linearly scanned and the garbled circuit was used to compare gene sequence of user with all gene sequences in database. The above scheme can achieve genetic comparison under the premise of protecting user privacy of both parties. However, the scheme needs to scan whole database with time complexity of O( n), and is inefficient when the genome database is large. In order to improve the efficiency of genetic comparison, a genetic comparison scheme based on Oblivious Random Access Memory (ORAM) was further proposed, in which genetic data was stored at ORAM first, then only the data blocks on target path were picked out to perform genetic comparison by using garbled circuit. This scheme has the number of comparisons sub-linear to the size of database and time complexity of O (log n). The experimental results show that the genetic comparison scheme based on ORAM reduces the number of comparisons from O( n) to O(log n) while realizing privacy protection, significantly decreases the time complexity of comparison operation. It can be used for disease diagnosis, especially in the case with large genome database.