A new three-dimensional variable-node element is proposed to achieve an efficient connection of non-matching interfaces between dissimilar finite element meshes. The variable-node elements at interfaces are compatible with conventional finite elements, and satisfy the interface conditions of continuity, and completeness across non-matching meshes. The present method thereby provides a seamless connection between dissimilar finite element meshes and a correct load transfer across non-matching interfaces. Therefore, it leads to an efficient approach for solving a class of problems involving the non-matching interfaces such as fluid solid interaction problems. Numerical examples are presented to show the effectiveness of the present method for solving fluid solid interaction problems with non-conforming interfaces, and the usefulness and application of the present method are discussed.