One embodiment of the present invention provides a system for facilitating multi-path load balancing at a local node in a network. During operation, the system measures a value for a metric on a local link which couples the local node to a neighboring node. In addition, the system receives from the neighboring node a neighbor path-metric value which indicates a value for the metric associated with all paths from the neighboring node to a destination node. The system then computes a "local path-metric value" for the metric associated with all paths from the local node to the destination node via the local link and the neighboring node. The system further computes a "packet-forwarding probability" corresponding to the destination node for each local link coupled to the local node, wherein the distribution of the packet-forwarding probability bears a nonlinear relation to the distribution of the local path-metric values for all the local links. The system subsequently forwards a packet destined for the destination node to one of the local links based on the computed packet-forwarding probability for that local link.