ABSTRACT Emulation of the Global (sky-averaged) 21-cm signal with neural networks has been shown to be an essential tool for physical signal modelling. In this paper, we present globalemu, a Global 21-cm signal emulator that uses redshift as a character-defining variable alongside a set of astrophysical parameters to estimate the signal brightness temperature. Combined with physically motivated data pre-processing, this makes for a reliable and fast emulator that is relatively insensitive to the network design. globalemu can emulate a high-resolution signal in 1.3 ms in comparison to 133 ms, a factor of 102 improvement, when using the existing public state-of-the-art 21cmGEM. We illustrate, with the standard astrophysical models used to train 21cmGEM, that globalemu is almost twice as accurate and for a test set of ≈1700 signals we achieve a mean root mean squared error of 2.52 mK across the band z = 7–28 ≈10 per cent the expected noise of the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH). The models are parametrized by the star formation efficiency, f*, minimum virial circular velocity, Vc, X-ray efficiency, fX, cosmic microwave background optical depth, τ, the slope and low energy cut-off of the X-ray spectral energy density, α and νmin, respectively, and the mean free path of ionizing photons, Rmfp. globalemu provides a flexible framework for easily emulating updated simulations of the Global signal and in addition the neutral fraction history. The emulator is pip installable and available at https://github.com/htjb/globalemu. globalemu will be used extensively by the REACH collaboration.