The invention discloses a semiactive control algorithm for a building structure under earthquake action by a frictional damper. The steps are as follows: firstly, a structural model is selected; secondly, the structure is calculated by the linear quadrics (LQR) classic and optimal control algorithm, and the optimal controlling force during the minimum energy of the building structure is designed; thirdly, the optimal controlling force is utilized for respectively designing the real-time variable damping and the variable stiffness of the frictional damper, and therefore the semiactive frictional controlling force of the frictional damper can be obtained by the calculation and the semiactive control to the building structure is realized; and fourthly, the semiactive controlling force of the frictional damper is utilized for controlling the building structure, and the vibratory response which is returned by the building structure under the earthquake action is collected. Indicated by the result of the numerical experiment, the algorithm of the invention is much more effective in controlling the dynamic response of a multi-story building structure, and solves the problem of poor effect of the prior art on controlling the acceleration response of the building structure; and with the increase of storeys, the advantage on acceleration control of the building structure under the earthquake action is much more obvious.