In view of poor performance of Coyote Optimization Algorithm (COA), a Best and Worst coyotes strengthened COA (BWCOA) was proposed. Firstly, for growth of the worst coyote in the group, a global optimal coyote guiding operation was introduced on the basis of the optimal coyote guidance to improve the social adaptability (local search ability) of the worst coyote. Then, a random perturbation operation was embedded in the growth process of the optimal coyote in the group, which means using the random perturbation between coyotes to promote the development of the coyotes and make full play of the initiative of each coyotes in the group to improve the diversity of the population and thus to enhance the global search ability, while the growing pattern of the other coyotes kept unchanged. BWCOA was applied to complex function optimization and Quadratic Assignment Problem (QAP) using hospital department layout as an example. Experimental results on CEC-2014 complex functions show that compared with COA and other state-of-the-art algorithms, BWCOA obtains 1.63 in the average ranking and 1.68 rank mean in the Friedman test, both of the results are the best. Experimental results on 6 QAP benchmark sets show that BWCOA obtains the best mean values for 5 times. These prove that BWCOA is more competitive.