  With the Schwinger's proper-time formalism of the Nambu-Jona-Lasinio model,
we investigate the finite volume effects in the presence of magnetic fields.
Since the coupling constant $G$ can be influenced by strong magnetic fields,
the model is solved with a running coupling constant $G(B)$ which is fitted by
the lattice average $(\Sigma_u+\Sigma_d)/2$ and difference $\Sigma_u-\Sigma_d$.
The investigation mainly focuses on the constituent quark mass and the thermal
susceptibility depending on the magnetic fields, the temperatures and the
finite sizes. For the model in finite or infinite volume, the magnetic fields
can increase the constituent quark mass while the temperatures can decrease it
inversely. There is a narrow range of the box length that makes the effects of
finite volume perform prominently. The model will behave close to infinite
volume limit for larger box length. It is shown that the influence of finite
volume can be changed by magnetic fields and temperatures. Finally, we discuss
the thermal susceptibility depending on the temperature in finite volume in the
presence of magnetic fields.
