Context. The asteroseismic exploitation of long period, g-mode hot B subdwarf pulsators (sdBV s ), undermined so far by limitations associated with ground-based observations, has now become possible, thanks to high quality data obtained from space such as those recently gathered with the CoRoT (COnvection, ROtation, and planetary Transits) satellite. Aims. We propose a detailed seismic analysis of the sdBV s star KPD 0629-0016, the first compact pulsator monitored with CoRoT, using the g-mode pulsations recently uncovered by that space-borne observatory during short run SRa03. Methods. We use a forward modeling approach on the basis of our latest sdB models, which are now suitable for the accurate computation of the g-mode pulsation properties. The simultaneous match of the independent periods observed in KPD 0629-0016 with those of the models leads objectively to the identification of the pulsation modes and, more importantly, to the determination of the structural and core parameters of the star.Results. The optimal model we found closely reproduces the 18 observed periods retained in our analysis at a 0.23% level on average. These are identified as low-degree ( = 1 and 2), intermediate-order (k = −9 through −74) g-modes. The structural and core parameters for KPD 0629-0016 are the following (formal fitting errors only): T eff = 26 290 ± 530 K, log g = 5.450 ± 0.034, M * = 0.471 ± 0.002 M , log (M env /M * ) = −2.42 ± 0.07, log (1 − M core /M * ) = −0.27 ± 0.01, and X core (C+O) = 0.41 ± 0.01. We additionally derive an age of 42.6 ± 1.0 Myr after the zero-age extreme horizontal branch, the radius R = 0.214 ± 0.009 R , the luminosity L = 19.7 ± 3.2 L , the absolute magnitude M V = 4.23 ± 0.13, the reddening index E(B − V) = 0.128 ± 0.023, and the distance d = 1190 ± 115 pc. Conclusions. The advent of high-precision time-series photometry from space with instruments like CoRoT now allows as demonstrated with KPD 0629-0016 the full exploitation of g-modes as deep probes of the internal structure of these stars, in particular for determining the mass of the convective core and its chemical composition.