  We present a new model for gamma-ray bursts (GRBs) that are not only
associated with supernovae but also have small baryon contamination. In this
model, we assume a newborn neutron star to move outward at a kick velocity of
$\sim 10^3 {\rm km} {\rm s}^{-1}$ in the supernova ejecta. We find that such a
neutron star still hypercritically accretes its surrounding supernova matter.
Once the stellar mass increases to some critical mass, the neutron star will
undergo a phase transition to become a strange star, leading to an energy
release of a few $10^{52}$ ergs. The phase transition, if possibly occuring
just near the supernova front, will first result in an ultra-relativistic
fireball and then a GRB. This provides a plausible explanation for the
GRB-supernova association. We estimate the burst rate to be $\sim 10^{-6}$ per
year per galaxy. Our model also predicts other possiblities. For example, if
the resulting fireballs have a Lorentz factor of the order of a few, they will
produce X-ray GRBs observed by BeppoSAX. We find the rate of such bursts to be
$\sim 10^{-5}$ per year per galaxy.
