Inter-Cloud federation is expected to form the next wave of technical development that may greatly enhance Cloud service provisioning. Networking plays a crucial role in an Inter-Cloud environment and has a significant impact on Cloud service performance. Software-defined networking is an indispensable ingredient in a Software-Defined Inter-Cloud Environment (SDICE). Selecting the appropriate network services for meeting performance requirements of Cloud applications is a key to realizing a high-performance SDICE. However, network resource abstraction and inter-domain networking in a SDICE bring in new challenges to performance-based network service selection. In order to tackle this challenging problem, we propose a novel network service selection approach in this paper. The key elements of this approach include a profile that abstracts network service capabilities, a general profile for Cloud applications to specify networking demands, and an analysis technique developed based on the capability and demand profiles for evaluating network service performance guarantee. Application of network calculus in this paper makes the developed approach agnostic to network implementations; therefore supports network abstraction enabled by the software-defined control plane in a SDICE.