Design and analysis of algorithm is one of the core component of implementation of any software. Its a very pivotal part. It is important to plan and design the most efficient algorithm for solving a problem. There are various means of algorithms to solve a problem, but the challenge here is to choose the most effectual and well organised algorithm. This manuscript indeed describes the concatenation of list of elements using a linear method called concat_vetc() function and concatenates two or more vectors, further the same functionality is being executed by using concat_assign_vect() function simplified assignment operation, in addition to it the time complexity of the function is being calculated to examine the performance of both the algorithms. The purpose is to provide efficient algorithm for concatenation of more than one vector.