In spite of recent significant research into various two-dimensional (2D) materials after the emergence of graphene, the development of a new 2D material that provides both high mobility and an appropriate energy band gap (which are crucial for various device applications) remains elusive. In this report, we demonstrate that the carrier transport behaviour of 2D Ti2CTx, which belongs to the family of 2D transition metal carbides and nitrides, can be tuned by modifying the surface group Tx (-OH, -F, and -O). Our results show that 2D Ti2C(OH)xFy and Ti2COx films can be obtained via simple chemical treatment, thermal annealing, and mechanical exfoliation processes. For the first time, we study the carrier transport properties of 2D Ti2CTx field effect transistors (FETs), obtaining the high field effect carrier mobilities of 10(4) cm(2) V(-1) s(-1) at room temperature. The temperature dependent resistivity of the Ti2COx film exhibits semiconductor like Arrhenius behaviour at zero gate voltage, from which we estimate the energy gap of 80 meV. One interesting feature of the FETs based on transition metal carbides is that the field effect mobility at room temperature is less sensitive to the measured transport gaps, which may arise from the dominant charge transport of activated carriers over the narrow energy gaps of the transition metal carbides. Our results open up the possibility that new 2D materials with high mobilities and appropriate band gaps can be achieved, and broaden the range of electronic device applications of Ti2CTx films.