The interaction of intense femtosecond laser pulses with atomic Argon clusters has been investigated by using nanoplasma model. Based on the dynamic simulations, ionization process, heating, and expansion of a cluster after irradiation by femtosecond laser pulses at intensities up to 2 $\times$ 1017 Wcm−2 are studied. The analytical calculation provides ionization rate for different mechanisms and time evolution of the density of electrons for different pulse shapes. In this approach, the strong dependence of laser intensity, pulse duration, and laser shape on the electron energy, the electron density, and the cluster size is presented using the intense chirped laser pulses. Based on the presented theoretical modifications, the effect of chirped laser pulse on the complex dynamical process of the interaction is studied. It is found that the energy of electrons and the radius of cluster for the negatively chirped pulses are improved up to 20% in comparison to the unchirped and positively chirped pulses.