In this study, we examine the new spherically symmetric wormhole solutions in modified symmetric teleparallel (f(Q)) gravity theory. Using the Morris-Thorne method, we construct traversable wormholes with a physically reasonable energy condition and investigate their stability under small perturbations. We discuss two wormhole geometries under the linear functional form of f(Q) with two distinct shape functions. Our results show that the violations of energy conditions in f(Q) gravity provide a viable framework for the study of wormholes. We analyze the properties of wormholes and their behavior under different conditions such as energy conditions, equilibrium conditions, and volume integral quantifiers to check the stability of wormholes. By using the anisotropy parameter, we observed that model-I is attractive in nature and model-II is attractive and repulsive both varying according to the value of r and constant parameters.