This paper deals with realization of fractional-order impedance functions by passive electrical networks composed of a fractional capacitor and some RLC components. The necessary and sufficient conditions for the existence of such a realization are found in a general case. Also for impedance functions described by a class of fractional-order transfer functions, the realizability conditions are stated as some algebraic conditions on the parameters of the transfer function. Moreover, a procedure is proposed for implementation of such impedance functions by passive electrical networks composed of a fractional capacitor and some RLC components. Numerical examples are presented to show the usefulness of the results of the paper in design of fractional-order electrical circuits.