The Web today has gone far beyond a tool for simply posting and retrieving information, but a universal platform to accomplish various kinds of tasks in daily life. However, research and application of personalized recommendation are still mostly restricted to intra-site vertical recom-menders, such as video recommendation in YouTube, or product recommendation in Amazon. Usually, they treat users' historical behaviors as discrete records, extract collaborative relations therein, and provide intra-site homogeneous recommendations, without specific consideration of the underlying tasks that inherently drive users' browsing actions. In this paper, we propose task-based recommendation to offer cross-site heterogenous item recommendations on a Web-scale, which better meet users' potential demands in a task, e.g., one may turn to Amazon for the dress worn by an actress after watching a video on YouTube, or may turn to car rental websites to rent a car after booking a hotel online. We believe that task-based recommendation would be one of the key components to the next generation of universal web-scale recommendation engines. Technically, we formalize tasks as demand sequences embedded in user browsing sessions, and extract frequent demand sequences from large scale browser logs recorded by a well known commercial web browser. Based on these demand sequences, we predict the upcoming demand of a user given the current browsing session, and further provide personalized heterogeneous recommendations that meet the predicted demands. Extensive experiments on cross-site heterogenous recommendation with real-world browsing data verified the effectiveness of our framework.