A solvable three-dimensional deterministic map that shows on-off intermittency is derived from a coupled mapping system. The distribution of an on-off variable, that of laminar duration, and the mean laminar duration are analytically obtained. The map enables us to discuss the probability measure on the attractor, which also gives the singularity spectrum f(\ensuremath{\alpha}). The singularity of the measure caused by the on-off intermittency give rises to a linear part of the spectrum f(\ensuremath{\alpha}).