The discovery of early bumps in some type-I superluminous supernovae (SLSNe-I) before the main peaks offers an important clue to their energy source mechanisms. In this paper, we updated an analytic magnetar-powered model for fitting the multiband light curves of double-peaked SLSNe-I. The early bump is powered by magnetar-driven shock-breakout thermal emission, and the main peak is powered by a radiative diffusion through the supernova (SN) ejecta as in the standard magnetar-powered model. Generally, the diffusive luminosity is greater than the shock-breakout luminosity at the early time, which usually makes the shock-breakout bumps unclear to observe. To obtain a clear double-peaked light curve, inefficient magnetar heating at early times is required. This model is applied to three well-observed double-peaked SLSNe-I (i.e., SN2006oz, LSQ14bdq, and DES14Xtaz). We find that a relatively massive SN ejecta with M-ej similar or equal to 10.2-18.1M(circle dot) and relatively large kinetic energy of SN ejecta erg are required, and the thermalization efficiency of the magnetar heating is suppressed before t(delay), which is in the range of similar or equal to 15-43 days. The model can reproduce the observed light curves well, with a reasonable and similar set of physical parameters for both the early bump and the main peak, strengthening support for the magnetar-powered model. In the future, modeling of the double-peaked SLSNe-I will become more feasible as more events are discovered before the early bump.