The author defines all fuzzy number which are symmetric respect to y-axis as zero fuzzy number，onthe basis，the author defines the limitation of complex fuzzy-valued function and discusses the properties ofconvergence. This eater obtains a series of results about limited complex fuzzy -valued function，including thelimitation of complex fuzzy-valued function is unique，the limited complex fuzzy-valued function has localboundedness and local protection，as well as the linear operation properties of the limitation. Furthermore，theconvergence criterion and the Cauchy convergence criterion of complex fuzzy-valued function are given. In thispaper，it is shown that the complex fuzzy-valued function is defined in a complex fuzzy set F( C)which valued thecomplex fuzzy number in F( C)(set of all complex fuzzy number ).