  We attempt to study a singularity-free model for the spherically symmetric
anisotropic strange stars under Einstein's general theory of relativity by
exploiting the Tolman-Kuchowicz metric. Further, we have assumed that the
cosmological constant $\Lambda$ is a scalar variable dependent on the spatial
coordinate $r$. To describe the strange star candidates we have considered that
they are made of strange quark matter (SQM) distribution, which is assumed to
be governed by the MIT bag equation of state. To obtain unknown constants of
the stellar system we match the interior Tolman-Kuchowicz metric to the
exterior modified Schwarzschild metric with the cosmological constant, at the
surface of the system. Following Deb et al. we have predicted the exact values
of the radii for different strange star candidates based on the observed values
of the masses of the stellar objects and the chosen parametric values of the
$\Lambda$ as well as the bag constant $\mathcal{B}$. The set of solutions
satisfies all the physical requirements to represent strange stars.
Interestingly, our study reveals that as the values of the $\Lambda$ and
$\mathcal{B}$ increase the anisotropic system becomes gradually smaller in size
turning the whole system into a more compact ultra-dense stellar object.
