Recent observations have detected galaxies at high-redshift z \sim 6 - 11 , and revealed the diversity of their physical properties , from normal star-forming galaxies to starburst galaxies . To understand the properties of these observed galaxies , it is crucial to understand the star formation ( SF ) history of high-redshift galaxies under the influence of stellar feedback . In this work , we present the results of cosmological hydrodynamic simulations with zoom-in initial conditions , and investigate the formation of the first galaxies and their evolution towards observable galaxies at z \sim 6 . We focus on three different galaxies which end up in halos with masses M _ { h } = 2.4 \times 10 ^ { 10 } ~ { } h ^ { -1 } { M _ { \odot } } ( Halo-10 ) , 1.6 \times 10 ^ { 11 } ~ { } h ^ { -1 } { M _ { \odot } } ( Halo-11 ) and 0.7 \times 10 ^ { 12 } ~ { } h ^ { -1 } { M _ { \odot } } ( Halo-12 ) at z = 6 . Our simulations also probe impacts of different sub-grid assumptions , i.e. , SF efficiency and cosmic reionization , on SF histories in the first galaxies . We find that star formation occurs intermittently due to supernova ( SN ) feedback at z \gtrsim 10 , and then it proceeds more smoothly as the halo mass grows at lower redshifts . Galactic disks are destroyed due to SN feedback , while galaxies in simulations with no-feedback or lower SF efficiency models can sustain galactic disk for long periods \gtrsim 10 ~ { } Myr . The expulsion of gas at the galactic center also affects the inner dark matter density profile . However , SN feedback does not seem to keep the shallow profile of dark matter for a long period . Our simulated galaxies in Halo-11 and Halo-12 reproduce the star formation rates ( SFR ) and stellar masses of observed Lyman- \alpha emitters ( LAEs ) at z \sim 7 - 8 fairly well given observational uncertainties . In addition , we investigate the effect of UV background radiation on star formation as an external feedback source , and find that earlier reionization extends the quenching time of star formation due to photo-ionization heating , but does not affect the stellar mass at z = 6 .