To improve the accuracy of hemispherical resonator gyro (HRG) output errors, a novel fusion algorithm is proposed based on improved support function and multi-dimensional dynamic time warping. By analyzing the temperature characteristics and big data characteristics of HRG, the eigenvectors are initially selected, and the correlation and redundancy are later removed by Kernel principal component analysis. To obtain potential relationships between different time series, an improved support function based on grey incidence analysis theory is brought in to reduce the computational complexity, and the genetic algorithm is introduced to identify the optimal parameters rather than manually setting them. To accurately quantify how similar or different a time series is compared with another, multi-dimensional dynamic time warping which utilizes Mahalanobis distance is introduced instead of dynamic time warping. Experiment results show that the proposed algorithm performs better in both accuracy and universality compared with the other three comparative methods.