  The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied
by means of exact solutions and the tensor renormalisation group (TRG) method.
The zero-field phase diagrams are obtained, where three phases such as
ferromagnetic, ferrimagnetic and paramagnetic phases, along with the
second-order phase transitions, have been identified. The TRG results are quite
accurate and reliable in comparison to the exact solutions. In a magnetic
field, the magnetization ($m$), susceptibility and specific heat are studied by
the TRG algorithm, where the $m=1/3$ plateaux are observed in the magnetization
curves for some couplings. The experimental data of susceptibility for the
complex Co(N$_3$)$_2$(bpg)$\cdot$ DMF$_{4/3}$ are fitted with the TRG results,
giving the couplings of the complex $J=22K$ and $J'=33K$.
