A novel bio-inspired algorithm called Orca Predation Algorithm (OPA) is proposed in this paper. OPA simulates the hunting behavior of orcas and abstracts it into several mathematical models: including driving, encircling and attacking of prey. The algorithm assigns different weights to the phases of prey driving and encircling through parameter adjustment to balance the exploitation and exploration stages of the algorithm. In the attacking phase, after considering the positions of several superior orcas and some randomly selected orcas, the optimal solution can be approached without losing the diversity of the particles. In order to estimate the performance of OPA, 67 unconstrained benchmark functions were first employed, and then the efficiency of the algorithm was further evaluated on five constrained engineering optimization problems. Besides, the computational complexity, parameter sensitivity and four qualitative metrics of OPA were analyzed to evaluate the applicability of the algorithm. The experimental results demonstrate that OPA can generate more promising results with superior performance relative to other test algorithms on different search landscapes.