In this paper, we present the first extinction map of the Small Magellanic Cloud (SMC) constructed using the color excess at near-infrared wavelengths. Using a new technique named "X percentile method", which we developed recently to measure the color excess of dark clouds embedded within a star distribution, we have derived an E(J – H) map based on the SIRIUS and 6X Two Micron All Sky Survey (2MASS) star catalogs. Several dark clouds are detected in the map derived from the SIRIUS star catalog, which is deeper than the 6X 2MASS catalog. We have compared the E(J – H) map with a model calculation in order to infer the locations of the clouds along the line of sight, and found that many of them are likely to be located in or elongated toward the far side of the SMC. Most of the dark clouds found in the E(J – H) map have counterparts in the CO clouds detected by Mizuno et al. with the NANTEN telescope. A comparison of the E(J – H) map with the virial mass derived from the CO data indicates that the dust-to-gas ratio in the SMC varies in the range AV /N H = 1-2 × 10–22 mag H-1 cm2 with a mean value of ~1.5 × 10–22 mag H-1 cm2. If the virial mass underestimates the true cloud mass by a factor of ~2, as recently suggested by Bot et al., the mean value would decrease to ~8×10–23 mag H-1 cm2, in good agreement with the value reported by Gordon et al., 7.59 × 10–23mag H-1 cm2.