We report on comprehensive results identifying the ground state of a triangular-lattice structured YbZnGaO_{4} as a spin glass, including no long-range magnetic order, prominent broad excitation continua, and the absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature ac susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We suggest this conclusion holds also for its sister compound YbMgGaO_{4}, which is confirmed by the observation of spin freezing at low temperatures. We consider disorder and frustration to be the main driving force for the spin-glass phase.