Spatial range query is one of the most common queries in spatial databases, where a user invokes a query to find all the surrounding interest objects. Most studies in range search consider Euclidean distances to retrieve the result in low cost, but with poor accuracy (i.e., Euclidean distance less than or equal network distance). Thus, researchers show that range search in network distance retrieves the results with high accuracy but with a vast amount of network distance computations. However, both of these techniques retrieve all objects in a given radius with a high number of false hits. Yet, in many situations, retrieving all objects is not necessary, especially when there are already enough objects closer to the query point. Also, when the radius of the search increases, a demotion in the performance will occur. Hence, approximate results are valuable just as the exact result, and approximate results can be obtained much faster than the exact result and are less costly. In this paper, we propose two approximate range search methods in spatial road network, namely approximate range Euclidean restriction and approximate range network expansion, to reduce the number of false hits and the number of network distance computations in a considerable manner. After the verification, these two methods are shown to be robust and accurate.