We present the results of far-ultraviolet (FUV) observations of comet C/2001 Q4 (NEAT) obtained with Far-ultraviolet Imaging Spectrograph (FIMS) on board the Korean microsatellite STSAT-1, which operated at an altitude of 700 km in a sun-synchronous orbit. FIMS is a dual channel imaging spectrograph (S-channel 900-1150 ${AA}$, L-channel 1350-1710 ${AA}$, and ${lambda}/{Delta}{lambda}$ ~ 550 for both channels) with large image fields of view (S-channel $4.0^{circ}{ imes}4.6^{prime}$, L-channel $7.5^{circ}{ imes}4.3^{prime}$, and angular resolution ~ $5-10^{prime}$) optimized for the observation of diffuse emission of astrophysical radiation. Comet C/2001 Q4 (NEAT) were made in two campaigns during its perihelion approach between May 8 and 15, 2004. Based on the scanning mode observations in the wavelength band of 1400-1700 ${AA}$, we have constructed an image of the comet with an angular size of $5^{circ}{ imes}5^{circ}$, which corresponds to the central coma region. Several important fluorescence emission lines were detected including S I multiplets at 1429 and 1479 ${AA}$, C I multiplets at 1561 and 1657 ${AA}$, and the CO $A^1{Pi}-X^1{Sigma}^+$ Fourth Positive system; we have estimated the production rates of the corresponding species from the fluxes of these emission lines. The estimated production rate of CO was $Q_{CO}=(2.65{pm}0.63){ imes}10^{28}s^{-1}$, which is 6.2-7.4% of the water production rate and is consistent with earlier predictions. The average carbon production rate was estimated to be $Q_C={sim}1.59{ imes}10^{28}s^{-1}$, which is ~60% of the CO production rate. However, the observed carbon profile was steeper than that predicted using the two-component Haser model in the inner coma region, while it was consistent with the model in the outer region. The average sulfur production rate was $Q_S=(4.03{pm}1.03){ imes}10^{27}s^{-1}$, which corresponds to ~1% of the water production rate.