This note is devoted to investigating the stability and stabilization problems for continuous-time singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). In this GUTR singular model, each transition rate can be completely unknown or only its estimate value is known. In terms of a set of coupled linear matrix inequalities (LMIs), a sufficient condition is established to ensure the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent state-feedback controller is derived to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.