As an effective global optimization technique, artificial bee colony (ABC) algorithm has become one of the hottest research topics in the fields of evolutionary algorithms. However, the solution search equation is not rotationally invariant, which causes the problem that the performance of ABC is sensitive to the coordinate system. Although many improved ABC variants have been developed, they rarely considered the problem. Hence, to solve the problem, we propose a new ABC variant with bi-coordinate systems (BSABC), including the original coordinate system and the eigen coordinate system. The two coordinate systems own different characteristics: (1) the former one aims to maintain the population diversity, and (2) the latter one is to adapt the search to the fitness landscape of the problems. Based on the characteristics, in the BSABC, the two coordinate systems are used in the employed bee phase and onlooker bee phase, respectively. Meanwhile, two new solution search equations are designed by utilizing the elite information, and they are respectively performed in the two coordinate systems to further improve the algorithm performance. As another contribution of this study, in the scout bee phase, the multivariate Gaussian distribution is constructed to replace the original method to generate offspring, which is helpful to save the search experience. The performance of the BSABC is verified by extensive experiments on the CEC2013 test suite and one real-world optimization problem, and four well-established ABC variants and three other evolutionary algorithms are included in the performance comparison. The comparison results confirm that the BSABC shows competitive performance by achieving better results on the majority of test functions.