With the wide spread and deepening of service-oriented computing, more and more enterprises and organizations are constructing their applications by integrating third-party Web services in the cloud nowadays. Building high-quality applications has long been a critical research issue. Quality of service (QoS) prediction provides valuable information for making optimal Web service selection from a set of functionally equivalent candidate services. Commonly, collaborative filtering technique like matrix factorization (MF) is implemented for predicting unknown QoS values, and most of them are built via modeling user-service interaction based on QoS data directly or take side information such as geographical location, network autonomous region into account. Due to the overlook of the implicit but important wide-range characteristic of QoS data, existing MF methods might incur high users’ and services’ biases, and their prediction accuracy will not be good enough if we are faced with such wide-range of QoS data. In this work, we first investigate the wide-range characteristic among users and services via real-world Web service QoS dataset, and argue that such observed finding is an essential factor for accurate QoS prediction. We then propose a novel prediction model named Wide-Range Aware Matrix Factorization (WRAMF), which tackles the wide-range influence via bias information combination and an active function mapping explicitly. The proposed WRAMF model is advantageous to existing MF-based models, which optimizes the model by an adaptive learning rate strategy that guides WRAMF to approach the optimal solution accurately, and trains the model by a well-designed parallel stochastic gradient descent algorithm efficiently. Comprehensive experiments are conducted by employing real-world QoS dataset and empirical results show that our WRAMF significantly outperforms the state-of-the-art methods in terms of accuracy and efficiency.