We present a photometric study of stellar populations in the blue compact dwarf (BCD) galaxy SBS 1415+437 from the archival Hubble Space Telescope data. The resulting color-magnitude diagram (CMD) for stars reaches about 29^m in V and I filters and reveals not only a young stellar population of main sequence and blue and red supergiants but also an older evolved population of red giant and asymptotic giant branch stars. From the tip of the red giant branch (TRGB) a distance modulus was found to be m - M = 30.65±0.08^m, which corresponds to a distance D = 13.5±1.0 Mpc. The youngest stars concentrate to the bright H II region in the south-western part of SBS 1415+437 and show a clumpy distribution, while the older populations occupy the largest area, form the halo of the galaxy and distributed more evenly. Spatial distribution of young stars also shows an evidence for propagating star formation in the last 50 Myr from the northeast to the southwest with an average velocity of about 60 km/s. The TRGB of SBS 1415+437 has very blue color with (V - I) _TRGB ≈ 1.30, which gives different age estimates for the galaxy depending on the assumed metallicity: 1) if we assume that the galaxy initially had a very low metallicity ([Fe/H] = -2.4 from the photometric estimate in this work), its age appears to be no less than the ages of Galactic globular clusters (about 10 Gyr); 2) if the metallicity of SBS 1415+437 remained almost the same through the evolution and was equal to that taken from the emission lines of ionized gas ([Fe/H] = -1.3), the age of the galaxy does not exceed 2 Gyr.