We introduce a method to solve the MaxCut problem efficiently based on quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary updates and an initial state involving no entanglement, as well as an imaginary-time-dependent Hamiltonian interpolating between a given graph and a subgraph with two edges excised. We apply the method to thousands of randomly selected graphs with up to fifty vertices. We show that our algorithm exhibits a 93% and above performance converging to the maximum solution of the MaxCut problem for all considered graphs. Our results compare favorably with the performance of classical algorithms, such as the greedy and Goemans–Williamson algorithms. We also discuss the overlap of the final state of the QITE algorithm with the ground state as a performance metric, which is a quantum feature not shared by other classical algorithms.