This article proposes a new population-based optimization algorithm called the Tangent Search Algorithm (TSA) to solve optimization problems. The TSA uses a mathematical model based on the tangent function to move a given solution toward a better solution. The tangent flight function has the advantage to balance between the exploitation and the exploration search. Moreover, a novel escape procedure is used to avoid to be trapped in local minima. Besides, an adaptive variable step size is also integrated in this algorithm to enhance the convergence capacity. The performance of TSA is assessed in three classes of tests: classical tests, CEC benchmarks, and engineering optimization problems. Moreover, several studies and metrics have been used to observe the behavior of the proposed TSA. The experimental results show that TSA algorithm is capable to provide very promising and competitive results on most benchmark functions thanks to better balance between exploration and exploitation of the search space. The main characteristics of this new optimization algorithm is its simplicity and efficiency and it requires only a small number of user-defined parameters.