This paper proposes a novel technique enabling flow-level multi-path forwarding on a hop-by-hop packet switched network such as IP networks. Generally on such networks, any packet from a node toward a destination is forwarded along the same path, even if some of the packets belong to a different flow with different characteristics. Depending on the packet characteristics, to fulfill demands such as Traffic Engineering and QoS routing, flow-level multi-path fowarding allows explicit selection of the paths on which to send packets. Multi Protocol Label Switching(MPLS) technology has been used to perform this function so far. However, to apply MPLS on an existing IP network, all non-MPLS-enabled routers in the network must be replaced with MPLS-enabled routers. Therefore, the migration cost is generally expensive. This paper proposes a novel technique, called Flow-Mapping Explicit Host Routing(FMEHR),that performs the function without MPLS, using unused address spaces such as IP private addresses. In a FMEHR network, an unused address is assigned to a particular flow, the destination addresses of all packets belonging to the flow are swapped with the address at an ingress FMEHR router and these packets are forwarded along the host route path to the address. This paper discusses the FMEHR concept, its realization on an IP network and its characteristics.