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With the proliferation of Internet-of-Things and continuous growth in the number of web services at the Internet-scale, the service recommendation is becoming a challenge nowadays. One of the prime aspects influencing the service recommendation is the Quality-of-Service (QoS) parameter, which depicts the performance of a web service. In general, the service provider furnishes the value of the QoS parameters during service deployment. However, in reality, the QoS values of service vary across different users, time, locations, etc. Therefore, estimating the QoS value of service before its execution is an important task, and thus the QoS prediction has gained significant research attention. Multiple approaches are available in the literature for predicting service QoS. However, these approaches are yet to reach the desired accuracy level. In this paper, we study the QoS prediction problem across different users, and propose a novel solution by taking into account the contextual information of both services and users. Our proposal includes two key steps: (a) hybrid filtering and (b) hierarchical prediction mechanism. On the one hand, the hybrid filtering method aims to obtain a set of similar users and services, given a target user and a service. On the other hand, the goal of the hierarchical prediction mechanism is to estimate the QoS value accurately by leveraging hierarchical neural-regression. We evaluate our framework on the publicly available WS-DREAM datasets. The experimental results show the outperformance of our framework over the major state-of-the-art approaches.