Aiming at the problems that swarm intelligence optimization algorithms are easy to fall into local optimum as well as have low population diversity in the optimization process and are difficult to optimize high-dimensional functions， an Alternately Optimizing Algorithm based on Brownian-movement and Gradient-information （AOABG） was proposed. First， a global and local alternately optimizing strategy was used in the proposed algorithm， which means the local search was switched in the range of getting better and the global search was switched in the range of getting worse. Then， the random walk of uniform distribution probability based on gradient information was introduced into local search， and the random walk of Brownian motion based on optimal solution position was introduced into global search. The proposed AOABG algorithm was compared with Harris Hawk Optimization （HHO）， Sparrow Search Algorithm （SSA） and Special Forces Algorithm （SFA） on 10 test functions. When the dimension of test function is 2 and 10， the mean value and standard deviation of AOABG’s 100 final optimization results on 10 test functions are better than those of HHO， SSA and SFA. When the test function is 30-dimensional， except for Levy function where HHO performs better than AOABG but the mean value of the two is in the same order of magnitude， AOABG performs best on the other nine test functions with an increase of 4.64%-94.89% in the average optimization results compared with the above algorithms. Experimental results show that AOABG algorithm has faster convergence speed， better stability and higher accuracy in high-dimensional function optimization.