The Wi-Fi fingerprinting (WF) technique normally suffers from the RSS (Received Signal Strength) variance problem caused by environmental changes that are inherent in both the training and localization phases. Several calibration algorithms have been proposed but they only focus on the hardware variance problem. Moreover, smartphones were not evaluated and these are now widely used in WF systems. In this paper, we analyze various aspect of the RSS variance problem when using smartphones for WF: device type, device placement, user direction, and environmental changes over time. To overcome the RSS variance problem, we also propose a smartphone-based, indoor pedestrian-tracking system. The scheme uses the location where the maximum RSS is observed, which is preserved even though RSS varies significantly. We experimentally validate that the proposed system is robust to the RSS variance problem.