We report finding kiloparsec-scale radio emissions aligned with parsec-scale jet structures in the narrow-line Seyfert 1 (NLS1) galaxy Mrk 1239 using the Very Large Array and the Very Long Baseline Array. Thus, this radio-quiet NLS1 has a jet-producing central engine driven by essentially the same mechanism as that of other radio-loud active galactic nuclei (AGNs). Most of the radio luminosity is concentrated within 100 parsecs and overall radio morphology looks edge-darkened; the estimated jet kinetic power is comparable to Fanaroff--Riley Type I radio galaxies. The conversion from accretion to jet power appears to be highly inefficient in this highly accreting low-mass black hole system compared with that in a low-luminosity AGN with similar radio power driven by a sub-Eddington, high-mass black hole. Thus, Mrk 1239 is a crucial probe to the unexplored parameter spaces of central engines for a jet formation.