To solve the problem of high computation complexity in deterministic global optimization algorithms and low success ratio in stochastic global optimization algorithms, a population-based global optimization algorithm using abstract convex underestimate is proposed. The proposed algorithm combines the abstract convexity theory within the framework of population evolutionary algorithms. The first step of the algorithm is to construct the abstract convex underestimate relaxed model for the whole initial population. Then, relevant tightening underestimate information is used to safely eliminate invalid regions and to guide the population updating. Additionally, descent directions of supporting hyperplanes are employed for local enhancement. Finally, evolutionary information helps to update supporting hyperplanes. Numerical experiment results show the effectiveness of the proposed algorithm.