We present Ks -band light curves for 299 Cepheids in the Small Magellanic Cloud (SMC) of which 288 are new discoveries that we have identified using multi-epoch near-infrared photometry obtained by the VISTA survey of the Magellanic Clouds system (VMC). The new Cepheids have periods in the range from 0.34 to 9.1 days and cover the magnitude interval 12.9 <= Ks <= 17.6 mag. Our method was developed using variable stars previously identified by the optical microlensing survey OGLE. We focus on searching new Cepheids in external regions of the SMC for which complete VMC Ks-band observations are available and no comprehensive identification of different types of variable stars from other surveys exists yet.