The Lagrangian formalism for a massive Rarita-Schwinger field with spin 5 2 is investigated. We try to construct Lagrangians from which we can derive, by means of the variational principle, all the supplementary conditions as well as the Dirac-type equation for this field. It is shown that such Lagrangians do not exist, if we require (i) that they contain the field variables and their first order derivatives only, and (ii) that the symmetry nature with respect to the tensor suffices of the field be assumed from the outset. In view of this we propose Lagrangians which contain the field variables and their derivatives up to the second order. Such Lagrangians constitute a 9-complex parameter family, whose members transform among themselves under certain linear transformations for the field variables. The relativistic quantization is carried out for this field by the Umezawa-Taka-hashi method. The usual P ∗- symbol method leads us to the Feynman rules to evaluate S-matrix elements. The minimal electromagnetic interaction of this field is also discussed, and it is shown that S-matrix elements do not depend on the parameters mentioned above. It is expected that our formalism can be straightforwardly extended to the case of higher-spin fields.