Based on an equivparticle model incorporating both confinement and leading-order perturbative interactions, we fit the model parameters to the experimental masses of
\mathrmp 
,
\mathrmn 
,
\Lambda 
, and
\Delta 
. It is found that the equivparticle model well reproduces the mass spectra of light baryons. Distinctive correlations of the confinement strength
D
, the strong coupling constant
\alpha_\rms
, and quark mass factor
f
with respect to the perturbative strength
C
are obtained, which can be well approximated by analytical formulae. The color-magnetic part of one-gluon-exchange interaction plays a significant role on the mass spectra of light baryons, which causes a mass gap of up to 300 MeV between baryons with spins
J=1/2
and 3/2. By adopting different strong coupling constants for a pair of quarks with strangeness, the hyperon masses can be better described with the model parameters fitted to the masses of
\Sigma 
and
\Xi 
. The equivparticle model developed here with constrained parameter sets are then applicable to the investigation of exotic states such as
\mathrmud
QM nuggets, strangelets, and compact stars.