We observed the narrow-line quasar SDSS J094857.3+002225, which has the highest known radio loudness for a narrow-line Seyfert~1 galaxy (NLS1), at 1.7--15.4 GHz with the Very Long Baseline Array (VLBA). This is the first very-long-baseline interferometry (VLBI) investigation for a radio-loud NLS1. We independently found very high brightness temperatures from (1) its compactness in a VLBA image and (2) flux variation among the VLBA observation, our other observations with the VLBA, and the Very Large Array (VLA). A Doppler factor larger than 2.7--5.5 was required to meet an intrinsic limit of brightness temperature in the rest frame. This is evidence for highly relativistic nonthermal jets in an NLS1. We suggest that the Doppler factor is one of the most crucial parameters determining the radio loudness of NLS1s. The accretion disk of SDSS J094857.3+002225 is probably in the very high state, rather than the high/soft state, by analogy with X-ray binaries with strong radio outbursts and superluminal jets such as GRS 1915+105.