  Ultrahigh-energy cosmic rays are often characterized indirectly by analyzing
the properties of secondary cosmic ray particles produced in the collisions
with air nuclei, the particle number $N_\mu$ of muon and the depth of shower
maximum $X_\mathrm{max}$ after air shower cascade are mostly studied to infer
the energy and mass of the incident cosmic rays. While, researches have shown
that there is a significant excess comparing the observed number of muons
arriving at the ground from extensive air showers (EAS) with the simulations by
using the existing cosmic ray hadronic interaction model. To explain this muon
excess phenomenon, a new theoretical model, the gluon condensation model (GC
model), is introduced in this paper and simulated by using the AIRES engine. We
asumme that the GC effect appearing mainly in the first colliding of the
cascade, leads to a significant increase in the strangeness production,
accodingly, the production rate of kaons is improved appearantly. The model
assumes that only pions and kaons are the new prodcutions in the hadron
cascades. It is found that, considering the GC effect, the value of $n_K/n_\pi$
increases and more energy of the incident cosmic rays paticipate in hadron
cascades, and then increase the number of mouns finally. This model provides a
new theoretical possibility to explain the muon excess puzzle.
