  We present the production cross section of heavy quarks \sigma^{cc},
\sigma^{bb} and {\sigma^{tt}} at the next-to-leading order in the
electron-proton interaction by using the quarks and gluon distribution
functions at the initial scale Q^{2}_{0}. To do this, we use a fitted form of
the heavy quark coefficient functions for deep-inelastic lepton-hadron
scattering to obtain the structure functions of heavy quarks. Then, we
calculate the reduced cross section of heavy quarks by using the structure
functions and subsequently present the single differential and the integrated
cross section of heavy quarks at the center-of-mass energies of 319 GeV , 1.3
TeV and 3.5 TeV in the electron-proton collision. The obtained numerical
results of the cross section of the charm and beauty quarks are compared with
the HERA data, which is a combination from the results of the H1 and ZEUS
detectors, and with the predictions from H1PDF, MSTW2008 and MSRT03.
Furthermore, we present the production cross section of top quark as a direct
prediction from our calculations.
