ω-path partition problem is the generalization of path partition problem. It comes of broadcasting communication in parallel computer system, computer network and distributed control system. This problem can be described by graph theory terminology as follows. Let G=(V,E) be an undirected simple graph with nonnegative edge-weights, and ω≥0 be a real. {P₁, P₂, …, P_m} is called to be an ω-path partition of G if P₁, P₂, …, P_m are m pairwise vertex-disjoint paths of G such that , and V(P)()(1GVPVmii==Ui)≤ω (for all i=1, 2, …, m, where W(P_i)= ). The ω-path partition number of G is the smallest cardinality of ω-path partition of G. The ω-path partition problem of G is to find a minimum ω-path partition and the ω-path partition number of G. It is evident that ω-path partition problem for any graph is NP-complete by the NP-completeness of Hamiltonian path. In this paper, some properties of ω-path partition have been investigated for paths, trees and forests with nonnegative edge-weights respectively. Linear time algorithms have been presented to solve ω-path partition problem for any path and tree with nonnegative edge-weights respectively. Local realization techniques and complexities of these two algorithms have been discussed in detail. Based above algorithms, an O(n) algorithm has been designed to solve ω-path partition problems for forests with nonnegative edge-weights. The algorithms presented in this paper are concise, and require less time and space.