  Tur\'{a}n type extremal problem is how to maximize the number of edges over
all graphs which do not contain fixed forbidden subgraphs. Similarly, spectral
Tur\'{a}n type extremal problem is how to maximize (signless Laplacian)
spectral radius over all graphs which do not contain fixed subgraphs. In this
paper, we first present a stability result for $k\cdot P_3$ in terms of the
number of edges and then determine all extremal graphs maximizing the signless
Laplacian spectral radius over all graphs which do not contain a fixed linear
forest with at most two odd paths or $k\cdot P_3$ as a subgraph, respectively.
