  In this paper, the null geodesics and gravitational lensing in a nonsingular
spacetime are investigated. According to the nature of the null geodesics, the
spacetime is divided into several cases. In the weak deflection limit, we find
the influence of the nonsingularity parameter $q$ on the positions and
magnifications of the images is negligible. In the strong deflection limit, the
coefficients and observables for the gravitational lensing in a nonsingular
black hole background and a weakly nonsingular spacetime are obtained.
Comparing these results, we find that, in a weakly nonsingular spacetime, the
relativistic images have smaller angular position and relative magnification,
but larger angular separation than that of a nonsingular black hole. These
results might offer a way to probe the spacetime nonsingularity parameter and
put a bound on it by the astronomical instruments in the near future.
