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In this work, we study asymptotics of the genealogy of Galton-Watsonprocesses. Thus we consider a offspring distribution such that the rescaledGalton-Watson processes converges to a continuous state branching process(CSBP) with jumps. After we show that the rescaled height (or exploration)process of the corresponding Galton-Watson family tree, converges in afunctional sense, to the continuous height process that Le Gall and Le Janintroduced in 1998 on their paper "branching processes in L\'evy processes :The exploration process".

Convergence to a Continuous State Branching Process with jumps and Height Process