  We investigate the dependence of cosmological parameters on the number count
of peaks (local maxima and minima) in the cosmic microwave background (CMB)
sky. The peak statistics contains the whole information of acoustic
oscillations in the angular power spectrum $C_l$ over $l$-space and thus it can
place complementary constraints on the cosmological parameters to those
obtained from measurements of $C_l$. Based on the instrumental specifications
of Planck, we find that the number count of peaks can provide new constraints
on the combination of the matter density $\Omega_{\rm m}$ and the Hubble
parameter $h$ approximately scaled as $\Omega_{\rm m} h^{-4.9}$ for a flat
$\Lambda$CDM model with $\Omega_{m}=0.3$ and $h=0.7$. Therefore, we suggest
that combining it with the constraints from $C_l$ scaled as $\Omega_{m}h^{3.8}$
(or commonly $\Omega_{\rm m}h^2$) can potentially determine $\Omega_{\rm m}$ or
equivalently solve the cosmic degeneracy by the CMB data alone.
