  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 multi-band 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 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 makes the shock breakout
bumps usually not clearly seen as observed. 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 relative massive SN ejecta with
$M_{\mathrm{ej}} \simeq 10.2-18.1 M_{\odot}$ and relative large kinetic energy
of SN ejecta $E_{\mathrm{sn}} \simeq (3.8-6.5) \times 10^{51}$ erg are
required, and the thermalization efficiency of the magnetar heating is
suppressed before $t_{\mathrm{delay}}$, which are in the range of $\simeq 15-
43$ days. The model can well reproduce the observed light curves, with a
reasonable and similar set of physical parameters for both the early bump and
the main peak, strengthening support for 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.
