Several pieces of research during the last decade in intelligent perception are focused on the development of algorithms allowing vehicles to move efficiently in complex environments. Most of existing approaches suffer from either processing time which do not meet real-time requirements, or inefficient in real complex environment, which also does not meet the full availability constraint of such a critical function. To improve the existing solutions, an algorithm based on curved lane detection by using a Bayesian framework for the estimation of multi-hyperbola parameters is proposed to detect curved lane under challenging conditions. The general idea is to divide a captured image into several parts. The trajectory is modeled by a hyperbola over each part, whose parameters are estimated using the proposed hierarchical Bayesian model. Compared to the existing works in the state of the art, experimental results prove that our approach is more efficient and more precise in road marking detection.