In this article, owing to the concept of C∗-algebra, we define two new classes of contractive mappings and elicit the fixed point theorems of these mappings in C∗-algebra-valued metric spaces. Simultaneously, we notice the existence and uniqueness of fixed points for cyclic contractive mappings in the above said spaces. Also, our results generalize and unify several existing results in the literature. Moreover, we consider an example to illustrate the validity of the derived results. Finally, as an application, we provide the existence and uniqueness of solutions to a type of integral equations.