While AI agents surpass human performance in classical board games such as Chess, Go, and Shogi, many complex turn-based strategy (TBS) games, particularly those involving multiple actions per player turn, remain challenging due to their enormous branching factors and long planning horizons. Unlike single-action-per-turn games, TBS games like Civilization or TUBSTAP require sequencing multiple unit-level decisions per turn, resulting in state spaces where conventional algorithms like Monte Carlo Tree Search (MCTS) and Rolling Horizon Evolutionary Algorithms (RHEA) struggle to scale. We propose Turn-Based Evolutionary Tree Search (TBETS), a novel hybrid algorithm that combines the depth-oriented selection of MCTS with the population-based variation of evolutionary algorithms. Unlike standard MCTS, TBETS treats each tree node as a turn-start state and each branch as a full multi-action sequence. To manage the wide but shallow tree, TBETS applies evolutionary operations, mutation and crossover, to choose child nodes to search, enabling adaptive exploration in high-dimensional action spaces. In experiments conducted on the TUBSTAP platform, TBETS outperformed state-of-the-art baselines, including M-UCT, RHEA, and FH-EMCTS. Notably, TBETS achieved a \(>20\%\) higher win rate over RHEA on large 10-unit maps, and surpassed M-UCT by over \(50\%\) on 8-unit scenarios. These results demonstrate that TBETS is a scalable and effective approach for TBS games, particularly as complexity increases.