This paper studies the aperiodic sampled-data control problem of singular Markov jump systems under uncertain and unknown transition rates. First, taking into account the system information from x(tk) to x(tk+1), a novel two-sided looped mode-dependent Lyapunov–Krasovskii function (LKF) is constructed, which provides more freedom to test the feasibility of the LMI condition in the criterion. Based on this LKF and an improved integral inequality, a stochastic admissibility condition is given by linear matrix inequalities (LMIs), which is less conservative. Then, by using a lemma of equivalent set, a controller algorithm without equality constraint is proposed by LMIs to ensure the stability of the system. Finally, several examples are provided to verify the validity of the main results.