We present deep Hubble Space Telescope NICMOS 2 F160W band observations of the central 56 '' x 57 '' (14 pc x 14.25 pc) region around R136 in the starburst cluster 30Dor (NGC 2070) located in the Large Magellanic Cloud. Our aim is to derive the stellar initial mass function (IMF) down to similar to 1M(circle dot) 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 3 Myr 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 3 Myr isochrone and a constant star formation history from 2 to 4 Myr. We derive the IMF after correcting for incompleteness due to crowding. The faintest stars detected have a mass of 0.5 M-circle dot and the data are more than 50% complete outside a radius of 5 pc down to amass limit of 1.1M(circle dot) for 3 Myr old objects. We find an IMF of dN/dlogM alpha M-1.20 +/- 0.2 over the mass range 1.1-20 M-circle dot only slightly shallower than a Salpeter IMF. In particular, we find no strong evidence for a flattening of the IMF down to 1.1 M-circle dot at a distance of 5 pc from the center, in contrast to a flattening at 2 M-circle dot at a radius of 2 pc, reported in a previous optical HST study. We examine several possible reasons for the different results including the possible presence of mass segregation and the effects of differential extinction, particularly for the pre-main sequence sources. If the IMF determined here applies to the whole cluster, the cluster would be massive enough to remain bound and evolve into a relatively low-mass globular cluster.