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In this paper we consider an ergodic diffusion process with jumps whose driftcoefficient depends on an unknown parameter $\theta$. We suppose that theprocess is discretely observed at the instants (t n i)i=0,...,n with $\Delta$n= sup i=0,...,n--1 (t n i+1 -- t n i) $\rightarrow$ 0. We introduce anestimator of $\theta$, based on a contrast function, which is efficient withoutrequiring any conditions on the rate at which $\Delta$n $\rightarrow$ 0, andwhere we allow the observed process to have non summable jumps. This extendsearlier results where the condition n$\Delta$ 3 n $\rightarrow$ 0 was needed(see [10],[24]) and where the process was supposed to have summable jumps.Moreover, in the case of a finite jump activity, we propose explicitapproximations of the contrast function, such that the efficient estimation of$\theta$ is feasible under the condition that n$\Delta$ k n $\rightarrow$ 0where k > 0 can be arbitrarily large. This extends the results obtained byKessler [15] in the case of continuous processes. L{\'e}vy-driven SDE,efficient drift estimation, high frequency data, ergodic properties,thresholding methods.

Contrast function estimation for the drift parameter of ergodic jump diffusion process