In this paper, the one-part alkali-activated geopolymer was adopted as the soil binder to stabilize the soft clay under the one-dimensional compressive loading. Factors influencing the stiffness and strength of the one-part geopolymer stabilized soil such as the proportion of silicon-aluminum raw materials, the mass ratio of solid NaOH (NH) to raw materials and the water-binder ratio were taken into account. The stiffness development of the one-part geopolymer stabilized soft clay under one-dimensional compressive loading was investigated by an improved transducer system equipped with a pair of bender extender elements and the tactile pressure sensor, from which the time history of earth pressure coefficient (i.e., K0) and elastic wave velocity (i.e., the compression wave velocity VP and the shear wave velocity VS) of the stabilized soil sample could be measured, respectively. Furthermore, the unconfined compressive strength (UCS) of the stabilized soil sample cured under varied one-dimensional compressive loadings was tested to reveal the strength development of the geopolymer stabilized soil sample. Among different mixing proportions, the alkali-activated binary precursor [90% ground granulated blast furnace slag (GGBFS) and 10% fly ash (FA)] exhibits the highest performance in terms of the VS, VP and UCS of the geopolymer stabilized soil sample when the activator/precursor and water/solid ratio are 0.15 and 0.7 (i.e., the 4.67 mol/L of NH solution), respectively. The prediction of UCS for the one-part geopolymer stabilized soft clay was proposed and established based on the elastic wave velocity (i.e., VS and VP). The outcome of the current study sheds light on the practical use of the one-part alkali-activated geopolymer as a soil binder in ground improvement.