The β-decays of neutron-rich carbon,nitrogen and fluorine isotopes have been sys-tematically studied using the OXBASH shell Model.In the psd,spsd and spsdpf model space,we use the W BP interaction to calculate the half-lives and neutron emission probabilities of neutron-rich carbon and nitrogen isotopes,respectively.With the USD (W) and CW interactions,we calculate the half-lives and neutron emission probabilities of neutron-rich fluorine isotope in the sd model space,respectively.The calculated half-lives and neutron emission probabilities repro-duce recent experimental data very well.It seems to show that the particles of the neutron-rich carbon and nitrogen isotopes are mainly excited in the spsd space.The β-decay of 21N to the neutron bound states in 21O is mostly the first forbidden transition which makes the neutron emission probability increase.The theoretical calculation of β-decay of 25F to 25Ne with CW interaction shows that CW interaction is better than USD interaction.