In this paper, we investigate the strong gravitational lensing by the stationary, axially-symmetric black hole in Kerr-Taub-NUT spacetime in the strong field limit. The deflection angle of light ray and other strong deflection limit coefficients are obtained numerically and they are found to be closely dependent on the NUT charge n and spin a. The magnification and the positions of the relativistic images are computed. The caustics are studied and the results show that these caustics drift away from the optical axis, which is quite different from the Schwarzschild black hole case. Moreover, the intersections of the critical curves on the equatorial plane are obtained and it is shown that they increase with the NUT charge. These results show that there is a significant effect of the NUT charge on the strong gravitational lensing.