Floating-point exception usually brings unpredictable errors to applications, as it is fairly difficult to design software free of exceptions. Implementing an efficient exception handling approach is thus important. However, existing techniques, while focusing on handing integer overflow errors, are not floating-point oriented. Considering the fact that floating-point calculation reduces the integer overflow error, this study proposes a floating-point oriented exception handling approach for mathematical function written in assembly language. It first maps various exceptions into 64-bit floating-point numbers, and then stages the handling process into three parts on basis of their kernel computations. These stages are input parameter detection, which handles INV exception, specific code detection, which handles DZE and INF exceptions, and output parameter detection, which handles FPF and DNO exceptions. In the meanwhile, the paper presents a theoretical proof as well to illustrate the validity of such staging technique. More than 600 floating-point functions are extracted from the mathematical function library Mlib to test the performance for different systems. The evaluation shows that the proposed technique is capable to decrease the occupation of functions with floating-point exceptions from 90% to 0%, and the result demonstrates its high efficiency.