  We study the entrainment effect between superfluid neutrons and charge
neutral fluid (called the proton fluid) which is made of protons and electrons
in neutron star interior within the two fluid formalism and using a
relativistic model where baryon-baryon interaction is mediated by the exchange
of $\sigma$, $\omega$ and $\rho$ mesons. This model of strong interaction also
includes scalar self interactions. The entrainment matrix and entrainment
parameter are calculated using the parameter sets of Glendenning (GL) and
another non-linear (NL3) interaction. The inclusion of $\rho$ mesons strongly
influences the entrainment parameter ($\epsilon_{mom}$) in a superfluid neutron
star. The entrainment parameter is constant at the core and drops rapidly at
the surface. It takes values within the physical range.
