Variable filters are filters whose frequency characteristics can be continuously changed to suit the application at hand. The changing characteristics must be achieved readily without having to resort to redesigning the filter. Spectral parameters are used to control the filter's characteristics. In this paper the design of IIR Laguerre filters with variable characteristics is addressed. The stability of Laguerre filters can be easily ensured which makes the design easier than that for traditional IIR filters. The design technique utilises the recently reported frequency transformation method for fixed Laguerre filters and polynomial curve fitting for modelling the coefficient of the variable filters. Design examples of variable bandwidth narrowband filters are given.