  We systematically construct ghost-free higher-derivative actions of Abelian
vector supermultiplets in four-dimensional ${\cal N}=1$ global supersymmetric
theories. After giving a simple example which illustrates that a naive
introduction of a higher-derivative term gives rise to a ghost, we discuss
possible building blocks for a ghost-free action and explicitly show that their
bosonic parts have no ghost mode and the auxiliary field $\boldsymbol{D}$ does
not propagate. Higher-derivative terms yield higher powers of the auxiliary
field $\boldsymbol{D}$ in the actions, and the D-term equations of motion
consequently admit multiple solutions in general. We confirm that the
well-known supersymmetric Dirac-Born-Infeld action falls into this class. We
further give another example in which the standard quadratic kinetic term
(Maxwell term) is corrected by a quartic term of the field strength. We also
discuss possible couplings to matter fields and a deformed D-term potential.
