  We solve the Schr\"odinger equation for a charged particle in the non-uniform
magnetic field by using the Nikiforov-Uvarov method. We find the energy
spectrum and the wave function, and present an explicit relation for the
partition function. We give analytical expressions for the thermodynamic
properties such as mean energy and magnetic susceptibility, and analyze the
entropy, free energy and specific heat of this system numerically. It is
concluded that the specific heat and magnetic susceptibility increase with
external magnetic field strength and different values of the non-uniformity
parameter, $\alpha$, in the low temperature region, while the mentioned
quantities are decreased in high temperature regions due to increasing the
occupied levels at these regions. The non-uniformity parameter has the same
effect with a constant value of the magnetic field on the behavior of
thermodynamic properties. On the other hand, the results show that transition
from positive to negative magnetic susceptibility depends on the values of
non-uniformity parameter in the constant external magnetic field.
