The ground state and magnon excitation of a theoretical model proposed for a quasi-one-dimensional π-conjugated organic polymer ferromagnet are studied. Within the mean-field approximation, considering Hubberd repulsion and the hopping of the π electrons on the main chain and the unpaired electrons on the side radicals, the ground state of the system turns out to be a high-spin ferromagnetic state. The magnon excitation is investigated by the random-phase approximation (RPA), and a magnon excitation spectrum that includes an acoustic mode is obtained. The results of the calculations show that the Hubberd repulsion of the unpaired electrons on the side radicals as well as the hopping interaction between the π electrons on the main chain and the unpaired electrons on the side radicals make an impact on the acoustic mode which holds the property of the ferromagnetic magnon. The large Hubberd repulsion and hopping interaction are favourable to the stability of the ferromagnetic ground state of the system.