  We study the phenomenological implications of two minor zeros in neutrino
mass matrix using trimaximal mixing matrix. In this context, we analyse fifteen
possible cases of two minor zeros in neutrino mass matrix and found only two
cases, namely Class $A_1$ and Class $A_2$, that are compatible with the present
neutrino oscillation data. We present correlations of several neutrino
oscillation parameters and give prediction of the total neutrino mass, the
values of effective Majorana mass, the effective electron anti-neutrino mass
and CP violating Majorana phases for these two classes. We also explore the
degree of fine tuning in the elements of neutrino mass matrix for the allowed
classes. Moreover, we propose a flavor model within the seesaw model along with
$Z_{8}$ symmetry group that can generate such classes.
