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This paper studies the problems of the finite‐time stochastic boundedness (FTSB) and stabilisation for a class of discrete‐time Markovian jump non‐linear quadratic systems with incomplete information on transition probabilities. It is shown that the FTSB of the system can be ensured under some sufficient conditions derived. As a corollary, some sufficient conditions of the finite‐time stochastic stability for the non‐linear quadratic systems without exogenous disturbance are also established. Based on these results, stabilising mode‐dependent state feedback controllers are designed for Markovian jump non‐linear quadratic systems with/without exogenous disturbance, respectively. Consequently, the finite‐time stochastic stabilisation problem is resolved. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]