Aiming at the problem that individuals cross border and suffer from premature convergence in the bat algorithm, we propose an improved bat algorithm based on crossborder relocation and Gaussian mutation. The algorithm pulls the individuals which cross the solution boundary back into the solution space, and uses the crossborder relocation strategy to relocate. We then use the Gaussian mutation strategy to control the search range of individuals, and the population is radically searched around the optimal solution as the center, which enhances the local search and global optimization ability of the bat algorithm. Since the loudness and pulse frequency of the bat algorithm are inconsistent when bats approaching the target solution, which affects the continuous evolution ability of the algorithm, we introduce the linear gradient strategy to ensure that the updates of loudness and pulse frequency are compatible with the continuous evolution of the algorithm. We compare the optimization ability of the new algorithm with other algorithms under different position relationships in the solution space, and analyze the convergence stability of the new algorithm with the experimental data. Experimental results show that the proposed algorithm has better convergence speed and accuracy. In addition, the global optimization ability and high dimensional problem optimization ability of the algorithm demonstrate  good robustness.