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Risk assessment of power transmission systems against strong winds requires models that can accurately represent the realistic performance of the physical infrastructure. Capturing material nonlinearity, p-delta effects in towers, buckling of lattice elements, joint slippage, and joint failure requires nonlinear models. For this purpose, this study investigates the reliability of transmission line systems by utilizing a nonlinear model of steel lattice towers, generated in OpenSEES platform. This model is capable of considering various geometric and material nonlinearities mentioned earlier. In order to efficiently estimate the probability of failure of transmission lines, the current study adopts an advanced reliability method through Error rate-based Adaptive Kriging (REAK) proposed by the authors. This method is capable of significantly reducing the number of simulations compared to conventional Monte Carlo methods such that reliability analysis can be done within a reasonable time. Results indicate that REAK efficiently estimates the reliability of transmission lines with a maximum of 150 Finite Element simulations for various wind intensities.