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We propose a fast algorithm for the linear-quadratic control problem with probabilistic constraints that is repeatedly solved in stochastic model predictive control. Under the assumption of affine state feedback and Gaussian noise, the finite horizon control problem is converted to an equivalent deterministic problem using the mean and covariance matrix as the state. A line search interior point method is proposed to solve this optimization problem, where the step direction can be quickly computed via a Riccati difference equation. Numerical examples show that this algorithm has linear complexity in the horizon length.