The concept of quasi-zero-stiffness (QZS) vibration isolator was proposed in recent decades to improve the low-frequency isolation performance without increasing the static displacement. This work is devoted to the concrete realization of a QZS isolator by utilizing transverse groove springs. Firstly, the QZS isolator is theoretically analyzed and some dynamical indices are analytically calculated. Then, the transverse groove springs are designed and the isolator prototype is assembled; the QZS feature of the prototype is basically fulfilled. Finally, the experiments are conducted by means of an electrodynamic shaker which generates sinusoidal base excitation for the isolator prototype; the experimental results clearly show the good isolation performance of the QZS isolator and meanwhile reflect some practical factors that should be noticed in actual applications.