In this work, a composite spherical adsorbent, which employs potassium titanium silicate as an adsorption active component, and calcium alginate as a carrier, was successfully prepared. Scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) were used to characterize the adsorbent. The kinetics and thermodynamics of rubidium and cesium ions adsorption were investigated comprehensively, by considering the effects of initial concentration, temperature, solution pH, and coexisting NaCl. According to the determination coefficients, the pseudo second-order kinetic model provided an impressive and comparable correlation, and the second-order rate constant and the initial adsorption rate increase with increasing temperature. In general, the equilibrium adsorption amount increases with the increasing initial metal ion concentration, but decreases with increasing coexisting NaCl. The adsorption capacity keeps constant in the pH value range 3-12 and slightly fades when the temperature increases from 25 to 55 degrees C. Under similar conditions, rubidium and cesium show the similar adsorption amount. The adsorbent has a fast adsorption rate and an adsorption capacity of about 1.55 mmol g(-1) for rubidium and 1.47 mmol g(-1) for cesium when the initial metal ion concentration is 0.10 mol L-1. The composite adsorbent is effective for the adsorption of rubidium or cesium ions from simulated brines.