We present the Maxwell superalgebra, an N=1, D=4 algebra with two Majorana supercharges, obtained as the minimal enlargement of a Poincaré superalgebra containing the Maxwell algebra as a subalgebra. The new superalgebra describes the supersymmetries of generalized N=1, D=4 superspace in the presence of a constant Abelian supersymmetric field strength background. Applying the techniques of nonlinear coset realization to the Maxwell supergroup we propose a new kappa-invariant massless superparticle model providing a dynamical realization of the Maxwell superalgebra.