We carried out a deep near-infrared survey of a bright-rimmed molecular cloud, BRC 14 (IC 1848A). The 10 σ limiting magnitude of the survey is 17.7 mag 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 1 Myr. 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.