Abstract: Blind source separation （BSS） can be used to extract modal coordinate vibrations from structural vibration signals. Complexity pursuit （CP） is one of the classical methods for solving the BSS problem. To improve the computational efficiency of the CP algorithm， this paper proposes two enhancements： it uses the negative log function of a Gaussian distribution as a nonlinear function to estimate signal complexity and derives formulas for rapidly computing signal complexity and its gradient； it employs a subspace search-based gradient descent algorithm to calculate the optimal mixing vector in the reduced subspace. The new formulas only require the covariance matrix of mixed signals and the covariance matrix of time delays when computing complexity and its gradient， without using all signal data. Numerical examples and structural vibration data are employed to evaluate the proposed method. The results demonstrate that the fast complexity pursuit algorithm outperforms traditional methods in terms of computational efficiency and accurately separates structural modal coordinate vibrations.