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We investigate scaling ansatz with texture zeros within the framework of linear seesaw mechanism. In this variant of seesaw mechanism a simplified expression of effective neutrino mass matrix mν containing two Dirac type matrices (mD and mDS) and one Majorana type matrix (mRS) is obtained by virtue of neglecting the global U(1)L symmetry breaking term in the mass term of the Lagrangian. Along with the charged lepton mass matrix, the matrix mRS, too, is chosen in a diagonal basis whereas a scaling relation is incorporated in mD and mDS with different scale factors. Our goal in this work is to achieve a completely phenomenologically acceptable mν generated by combinations of mD and mDS containing least number of independent parameters or maximum number of zeros. At the end of the numerical analysis it is found that number of zeros in any of the constituent Dirac type matrices (mD and mDS) of mν cannot be greater than six in order to meet the phenomenological requirements. The hierarchy obtained here is normal and also the values of the two parameters sum mass (∑mi) and |mνee| are below the present experimental lower limit.