In this brief, the globally fixed-time control problem is investigated for a general class of uncertain nonlinear systems. The novelties of this brief are two folds. One novelty lies in the propose of a novel variable-gain second-order sliding mode (SOSM) controller. It overcomes the principal shortcomings of first-order sliding mode control and makes it possible to achieve fixed-time stability. The conventional SOSM algorithms can only achieve finite-time stability whose settling time will grow unboundedly when the initial conditions tend to infinity. Another novelty is the extension of constant upper bounds to time-varying upper functions. This enables us to propose a global result, while only local results can be obtained in most of the existing literatures. It is indicated that the proposed novel variable-gain SOSM controller can achieve the establishment of SOSMs in a fixed-time independent of initial conditions. In addition, Lyapunov analysis is given to show that the closed-loop system is globally fixed-time stable. An application to variable-length pendulum is given.