Since the membrane algorithm was proposed, it has been used for many optimization problems such as, traveling salesman problem, the knapsack problem, and so on. In membrane algorithms, the membranes have two functions: container and comparator. As a container, each membrane contains one evolutionary algorithm like genetic algorithm and ant colony algorithm. These algorithms are called sub-algorithms and used to evolve individuals. As a comparator, the membrane will compare the results of sub-algorithms, and select the best as the base of the next evolvement. This paper proposes a novel evolutionary algorithm called membrane evolutionary algorithm framework (MEAF). Unlike the presented membrane algorithms, the membranes in MEAF will be evolved to solve problems by using four operators that are abstracted from the life cycle of living cells. Based on MEAF, a membrane evolutionary algorithm called MEAMVC is proposed to solve the minimum vertex cover (MVC) problem. The experimental results show the advantages of MEAMVC when MEAMVC is compared with two state-of-the-art MVC algorithms proposed in recent years.