Electrical transmission tower-line systems form the backbone of our modern society, facilitating the seamless distribution of power over vast distances. The failure of any transmission tower among the line system can result in regional disruptions to power supply. Thunderstorm wind events pose significant threats to the structural integrity of transmission towers, making their fragility analysis crucial for ensuring the reliability and resilience of the power distribution systems. Deriving the fragility curve of transmission towers involves assessing the evolution of the joint probability density function of their responses. The structural response of these towers during the thunderstorm wind event always exhibits nonlinear characteristics; therefore, the nonlinear time-history analysis by using the finite element analysis is always adopted. However, conducting the time-history analysis for such scenarios is notably time-consuming, especially when combine the Monte Carlo simulation techniques and time-history analysis for fragility analysis. In the present study, an efficient procedure for the fragility analysis of the transmission tower subjected to bidirectional thunderstorm wind is described. The modeling of the wind field involves decomposing the thunderstorm wind into a time-varying mean wind velocity and a residual nonstationary fluctuation. The time-varying mean wind velocity is extracted from recorded thunderstorm wind data, and the variation along height is assumed to be proportional to the derived time-varying mean wind velocity. The nonstationary fluctuation is modeled as spatiotemporally varying by considering the incoherent effect and simulated using spectral representation method. For the modeling of the transmission tower, the uncertainty involved in yield strength and elastic modulus is considered. The proposed procedure incorporates a probability concentration-based simulation, combining aspects of the point estimate method and Latin hypercube sampling. Additionally, it employs a weighted (kernel) smoothing technique using simulated samples to estimate the evolution of joint probability density functions for tower responses. Finally, the time-dependent distribution of the transmission tower‘s top displacement subjected to thunderstorm wind is presented, demonstrating the effectiveness of the proposed procedure in assessing and understanding the vulnerability of these vital structures to such wind events.