In this paper, we propose a framework for privacy-preserving outsourced functional computation across large-scale multiple encrypted domains, which we refer to as POFD. With POFD, a user can obtain the output of a function computed over encrypted data from multiple domains while protecting the privacy of the function itself, its input and its output. Specifically, we introduce two notions of POFD, the basic POFD and its enhanced version, in order to tradeoff the levels of privacy protection and performance. We present three protocols, named Multi-domain Secure Multiplication protocol (MSM), Secure Exponent Calculation protocol with private Base (SECB), and Secure Exponent Calculation protocol ( SEC), as the core sub-protocols for POFD to securely compute the outsourced function. Detailed security analysis shows that the proposed POFD achieves the goal of calculating a user-defined function across different encrypted domains without privacy leakage to unauthorized parties. Our performance evaluations using simulations demonstrate the utility and the efficiency of POFD.