In this paper, we present a complex-valued neuro-fuzzy inference system (CNFIS) and its gradient descent based learning algorithm developed employing Wirtinger calculus. The proposed CNFIS is a four layered network which realizes zero-order Takagi-Sugeno-Kang based fuzzy inference mechanism. CNFIS is used to predict the speed and direction of wind. Here, the speed and direction are considered as statistically independent variables and are represented as a complex-valued signal (with speed as magnitude and direction as phase). Performance of CNFIS is compared with other algorithms available in the literature and results indicate improved performance of CNFIS. The major contribution of this paper is as follows: (1) Propose a complex-valued neuro-fuzzy inference system (2) Employ Wirtinger calculus for complex-valued gradient descent algorithm (3) Solve wind speed and direction prediction problem in complex domain.