Pricing cloud resources plays an important role in leading to the success of cloud computing. Cloud services are priced at different levels in infrastructure-as-a-service (IaaS) cloud market. For example, Amazon EC2 offers its cloud resources with three pricing schemes, the subscription model, pay-as-you-go model and spot pricing model. With more and more IaaS cloud service providers (CSPs) beginning to provide cloud services, they form a competitive market to compete for cloud users. Therefore, how to set optimal prices in order to maximize their revenue in a competitive IaaS cloud computing market while at the same time meeting the cloud users' demand satisfaction is a problem that CSPs should consider. Towards this end, in this paper, we study subscription pricing competition in a duopoly IaaS cloud computing market. First, we analyze whether or not the cloud users choose to use cloud service. Then, we present a game theoretic analysis of a cloud market with two CSPs competing non-cooperatively for cloud users.