In this paper, we propose a neural architecture search framework based on a similarity measure between the baseline tasks and the incoming target task. We first define the notion of task similarity based on the log-determinant of the Fisher Information Matrices. Next, we compute the task similarity from each of the baseline tasks to the incoming target task. By utilizing the relation between a target and a set of learned baseline tasks, the search space of architectures for the incoming target task can be significantly reduced, making the discovery of the best candidates in the set of possible architectures tractable and efficient, in terms of GPU days. This method eliminates the requirement for training the networks from scratch for the incoming target task as well as introducing the bias in the initialization of the search space from the human domain. Experimental results with 8 classification tasks in MNIST and CIFAR-10 datasets illustrate the efficacy of our proposed approach and its competitiveness with other state-of-art methods in terms of the classification performance, the number of parameters, and the search time.