Linear programming (LP) model of reactive-power optimization problem is solved by the most-obtuse-angle relaxation algorithm (MRA), in which trust region constraints on linear step sizes are added. Firstly，the concept of pivoting indices and its calculation formulae are defined according to most-obtuse-angle principle, and pivoting indices corresponding to inequality constraints are computed. Then inequality constraints in the original LP model are filtered based on these values of pivoting indices and a relaxed LP model is established. This relaxed model is solved by primal simplex method. If this solution from the relaxed model satisfies inequality constraints of the original LP model, the solution is final result expected. Otherwise，all the remaining inequality constraints in the relaxed LP model are added into the relaxed model to obtain the original model with changed order of inequality constraints. This original model is solved by dual simplex method. In essence, the MRA is a two-phase simplex method. Also solution in phase II can utilize solution obtained in phase I fully and hence computation efficiency is enhanced obviously. Results on five test systems and a 538-bus real system demonstrate effectiveness of the proposed algorithm by comparisons with simplex method and trust-region interior-point method.