For a class of second-order sub-fully actuated systems (SOSFASs), this paper presents a preset-trajectory-based (PT-based) adaptive stabilising control method by integrating the function augmented sliding mode control (FASMC) technique and the flat-zone introduced Lyapunov function technique. The SOSFASs under study are subject to internal uncertainties and external disturbances. The proposed PT-based stabilising control method exhibits several attractive features: 1) The system states can converge to a predefined region close to zero in a preassigned time and can be confined in a preassigned ‘safe’ area, which can make the control coefficient matrix always full rank so as to preserve the realizability of the proposed controller; 2) the utilization of flat-zone introduced Lyapunov function technique not only eliminates the chatting phenomenon, but also avoids the potential persistent increase problem of the adaptive law; and 3) the control gain increases as the adaptive law increases only when necessary, that is, when the current control gain is not sufficient to suppress uncertainties or disturbances, therefore, the conservativeness of the control design due to unnecessarily high control gain can be effectively reduced. The effectiveness of the proposed control method is verified via a numerical example.