  B[e] type stars are characterised by strong emission lines, photometric $\&$
spectroscopic variabilities and unsteady mass-loss rates. MWC 137 is a galactic
B[e] type star situated in the constellation Orion. Recent photometric
observation of MWC 137 by TESS has revealed variabilities with a dominant
period of 1.9 d. The origin of this variability is not known but suspected to
be from stellar pulsation. To understand the nature and origin of this
variability, we have constructed three different set of models of MWC 137 and
performed non-adiabatic linear stability analysis. Several low order modes are
found to be unstable in which models having mass in the range of 31 to 34
M$_{\odot}$ and 43 to 46 M$_{\odot}$ have period close to 1.9 d. The evolution
of instabilities in the non-linear regime for model having solar chemical
composition and mass of 45 M$_{\odot}$ leads to finite amplitude pulsation with
a period of 1.9 d. Therefore in the present study we confirm that this
variability in MWC 137 is due to pulsation. Evolutionary tracks passing through
the location of MWC 137 in the HR diagram indicate that the star is either in
post main sequence evolutionary phase or about to enter in this evolutionary
phase.
