Taking into account the SchusterToro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we supersymmetrize constrained formulation of the theory. In each formulation, we provide supersymmetry transformations for the N=1 supermultiplet in fourdimensional flat spacetime, in which continuous spin particle (CSP) is considered to be a complex scalar continuous spin field, and its superpartner which can be called " CSPino " is considered to be a Dirac continuous spin field. It is shown that the algebra of these supersymmetry transformations are closed onshell. Furthermore, we illustrate how these two separate set of transformations are related to each other. Finally, we investigate whether obtained supersymmetry transformations reproduce the known result of the higher spin gauge field theory in the helicity limit.
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