We have obtained deep J and K' images of four fields in and around the disk globular cluster M71. Our (K, J-K) diagram extends two magnitudes fainter than the main-sequence turn-off (MSTO), which occurs at K similar to 15.5. The near-infrared color-magnitude diagram (CMD) is compared with isochrones from Bergbusch and VandenBerg (1992, ApJS, 81, 163), which were transformed onto the near-infrared observational plane using two different methods. We find that isochrones translated onto the observational plane using relations derived from model atmospheres reproduce the slope of the red giant branch (RGB) on the (K, J-K) diagram from the sub-giant branch (SGB) to a point slightly brighter than the horizontal branch (HB), but do not match the observed color difference between the MSTO and the base of the RGB. On the other hand, models transformed using empirical relations derived from moderately metal-poor globular cluster and solar neighborhood stars closely match the morphology of the CMD near the MSTO. These models suggest that differential comparisons of near-infrared CMD's using, for example, the color difference between the MSTO and the base of the RGB, could be used to detect age differences comparable to what can be achieved at optical wavelengths. We also derive an age for M71 near 16 Gyr, although this conclusion should be considered as tentative given uncertainties in the metallicity of M71 and our knowledge of stellar physics. Finally, we investigate the mass function between 0.9 and 0.6 M. and find it to be relatively flat, in good agreement with what has been computed from observations shortward of 1 mu m.