A Distributed NetworkSystem (DNS) is a set of application and system programs, and data exchanges across a number of independent personal computers connected by a communication network. Task allocation in distributed network system is always a challenging task and also very helpful in order to enhance the performance of DNS. Although there are two types of approaches for task allocation and these are dynamic and static. Dynamic approach of task allocation is much appropriate manner and it also makes the best use of available computational power in DNS. Task allocation problem can be explained as ‘m’ number tasks are required to execute on ‘n’ number of processors where number tasks (m) is always greater than number of processors (n) (m>n). This research paper proposed a dynamic task allocation model to allocate the ‘m’ number of tasks on ‘n’ number of processors in distributed network system and execution completes in k number of phases. Proposed dynamic model will help to reduce the cost of task allocation. Phase wise execution cost, inter task communication cost, residing cost of each task on different processors, and reallocation cost for each task also have taken into the consideration to design a dynamic task allocation model.