The mass composition of ultra-high energy cosmic rays is important to understand their origin. The maximum depth of air shower developments, $X_{max}$, is one of the indicators of the mass composition. However, the prediction of $X_{max}$ depends on the choice of the hadronic interaction model, which makes it difficult to interpret the mass composition. Diffractive collision is a collision type of hadronic interactions and one of the proposed sources of this uncertainty. In this study, we estimate the effect of the fraction of the diffractive collision on the prediction of the mean of $X_{max}$ for the $10^{19}$ eV proton incident case by using air shower simulation package CONEX 5.64 and by artificially modifying the fraction of the diffractive collisions in the air shower simulation. The effect of the fraction difference among the major interaction models is estimated to be 8.9 g/cm$^2$, which is non-negligible. Furthermore, we demonstrate that even if the same fraction of diffractive collisions is used in the models, the discrepancy between the current models in the $X_{max}$ prediction does not reduce. Other sources of model discrepancy such as particle production after diffractive collisions must be studied more carefully.