We present deep Hubble Space Telescope NICMOS 2 F160W band observations of the central 56"x57" (14pcx14.25pc) region around R136 in the starburst cluster 30 Dor (NGC 2070) located in the Large Magellanic Cloud. Our aim is to derive the stellar initial mass function (IMF) down to ~1M_{sun} in order to test whether the IMF in a massive metal-poor cluster is similar to that observed in nearby young clusters and the field in our Galaxy. We estimate the mean age of the cluster to be 3Myr by combining our F160W photometry with previously obtained HST WFPC2 optical F555W and F814W band photometry and comparing the stellar locus in the color-magnitude diagram with main sequence and pre-main sequence isochrones. The color-magnitude diagrams show the presence of differential extinction and possibly an age spread of a few megayear. We convert the magnitudes into masses adopting both a single mean age of 3Myr isochrone and a constant star formation history from 2 to 4Myr. We derive the IMF after correcting for incompleteness due to crowding. The faintest stars detected have a mass of 0.5M{sun} and the data are more than 50% complete outside a radius of 5pc down to a mass limit of 1.1M{sun}_ for 3Myr old objects.