Abstract: Over more than a thousand years of research on simultaneous linear congruences in one variable, Chinese and foreign mathematicians have developed a world-renowned classic algorithm-Chinese Remainder Theorem. This classic algorithm can be run in computers to handle large values and large amounts of data quickly, and its efficiency far exceeds manual calculation. As an attempt to seek a more efficient way to solve simultaneous linear congruences in one variable than the classic algorithm, a new algorithm was proposed here. The new algorithm first constructed a basic strategy for solving the problem through trial and error. Then, variable replacement was progressively performed to find larger value with small value, in order to reduce the number of trials. Finally, an iterative algorithm was derived that can obtain the solution without any trial and error. Analysis and comparison with computer-calculated results show that the maximum data that can be processed by the new algorithm is several times, up to a thousand times, larger than those of the classic algorithm. In addition, the computation time required by the new algorithm to solve simultaneous linear congruences in one variable is reduced by over 25% compared to the classic algorithm.