  The purpose of our present work is to investigate some new features of a
static anisotropic relativistic hybrid compact star composed of strange quark
matter (SQM) in the inner core and normal baryonic matter distribution in the
crust. Here we apply the simplest form of the phenomenological MIT bag model
equation of state $p_q = \frac{1}{3}(\rho_q - 4B_g)$ to correlate the density
and pressure of strange quark matter within the stellar interior, whereas
radial pressure and matter density due to baryonic matter are connected by the
simple linear equation of state $p_r = \alpha \rho - \beta$. In order to obtain
the solution of the Einstein field equations, we have used the Tolman-Kuchowicz
{\em ansatz} [Tolman, Phys Rev 55:364, 1939; Kuchowicz, Acta Phys Pol 33:541,
1968] and further derivation of the arbitrary constants from some physical
conditions. Here, we examine our proposed model graphically and analytically in
detail for physically plausible conditions. In particular, for this
investigation, we have reported on the compact object Her $X-1$ [Mass=$(0.98
\pm 0.12)M_{\odot}$; Radius= $8.1_{-0.41}^{+0.41}$ km] in our paper as a
strange quark star candidate. In order to check the physical validity and
stability of our suggested model, we have performed various physical tests both
analytically and graphically, namely, dynamical equilibrium of applied forces,
energy conditions, compactness factor, and surface redshift etc. Finally, we
have found that our present model meets all the necessary physical requirements
for a realistic model and can be studied for strange quark stars (SQS).
