We carried out a deep near-infrared survey of a bright-rimmed molecular cloud, BRC 14 (IC 1848A). The 10{sigma} limiting magnitude of the survey is 17.7mag at the K-band. Seventy-four sources are classified as young stellar object (YSO) candidates based on a near-infrared color-color diagram. The faintest YSO candidates may have masses on the order of tenths of the solar mass, assuming an age of 1Myr. We examined three values as indicators of star formation: fraction of the YSO candidates, extinctions of all sources, and near-infrared excesses of the YSO candidates. All indicators increase from outside of the rim to the center of the molecular cloud, which suggests that the formation of the low-mass stars in the BRC 14 region proceeds from outside to the center of the cloud.