The data collection problem is one of the most important issues in Wireless Sensor Networks (WSNs). Constructing a tree from all sensor nodes to the sink node is the simplest way, but this raises the problem of energy unbalance since the sensors closer to the sink node would have much higher workloads from relaying data. To cope with the energy unbalance problem, a number of mobile-sink mechanisms have been proposed in recent years. This paper proposes an Energy-Balanced Data Collection mechanism, called EBDC, which determines the trajectory of a mobile data collector (or mobile sink) such that the data-relaying workloads of all sensors can be totally balanced. Theoretical analysis and performance evaluation reveal that the proposed EBDC mechanism outperforms the existing approaches in terms of network lifetime and the degree of energy balancing.