Cloud computing has emerged as a new computing paradigm and its economics has opened up a new research area. Though progress has been made toward address competitions among Cloud service providers (CSPs) or among network service providers (NSPs), few studies have focused on the relationship between CSPs and NSPs. In this paper, we investigate this problem and present a new economic model to characterize the competition between CSPs and NSPs. We then conduct thorough theoretical analysis and numeric experiments to validate the proposed model. The results show that the replacement coefficient, connection rate, service coefficient, the equilibrium will affect the market share and the profit of CSPs and NSPs. Through this study, we believe that the developed economic model is general and practical, thus it is applicable to model the Cloud computing market.