Aims. We study PTF11mnb, a He-poor supernova (SN) whose light curves resemble those of SN 2005bf, a peculiar double-peaked stripped-envelope (SE) SN, until the declining phase after the main peak. We investigate the mechanism powering its light curve and the nature of its progenitor star. Methods. Optical photometry and spectroscopy of PTF11mnb are presented. We compared light curves, colors and spectral properties to those of SN 2005bf and normal SE SNe. We built a bolometric light curve and modeled this light curve with the SuperNova Explosion Code (SNEC) hydrodynamical code explosion of a MESA progenitor star and semi-analytic models. Results. The light curve of PTF11mnb turns out to be similar to that of SN 2005bf until similar to 50 d when the main (secondary) peaks occur at -18.5 mag. The early peak occurs at similar to 20 d and is about 1.0 mag fainter. After the main peak, the decline rate of PTF11mnb is remarkably slower than what was observed in SN 2005bf, and it traces well the Co-56 decay rate. The spectra of PTF11mnb reveal a SN Ic and have no traces of He unlike in the case of SN Ib 2005bf, although they have velocities comparable to those of SN 2005bf. The whole evolution of the bolometric light curve is well reproduced by the explosion of a massive (M-ej = 7.8 M-circle dot), He-poor star characterized by a double-peaked Ni-56 distribution, a total Ni-56 mass of 0.59 M-circle dot, and an explosion energy of 2.2 x 10(51) erg. Alternatively, a normal SN Ib/c explosion (M(Ni-56) = 0.11 M-circle dot, E-K = 0.2 x 10(51) erg, M-ej = 1 M-circle dot) can power the first peak while a magnetar, with a magnetic field characterized by B = 5.0 x 10(14) G, and a rotation period of P = 18.1 ms, provides energy for the main peak. The early g-band light curve can be fit with a shock-breakout cooling tail or an extended envelope model from which a radius of at least 30 R-circle dot is obtained. Conclusions. We presented a scenario where PTF11mnb was the explosion of a massive, He-poor star, characterized by a double-peaked Ni-56 distribution. In this case, the ejecta mass and the absence of He imply a large ZAMS mass (similar to 85 M-circle dot) for the progenitor, which most likely was a Wolf-Rayet star, surrounded by an extended envelope formed either by a pre-SN eruption or due to a binary configuration. Alternatively, PTF11mnb could be powered by a SE SN with a less massive progenitor during the first peak and by a magnetar afterward.