We present theoretical model comparison with published ALICE results for D-mesons (D$^0$, D$^+$ and D$^{*+}$) in $p$+$p$ collisions at $sqrt{s}$ = 7 TeV and $p$+Pb collisions at $sqrt{s_{NN}}$ = 5.02 TeV. Event generator HIJING, transport calculation of AMPT and calculations from NLO(MNR) and FONLL have been used for this study. We found that HIJING and AMPT model predictions are matching with published D-meson cross-sections in $p$+$p$ collisions, while both under-predict the same in $p$+Pb collisions. Attempts were made to explain the $R_{pPb}$ data using NLO-pQCD(MNR), FONLL and other above mentioned models.