To explore the influence laws of random eccentricity on seismic capacity reliability of RC columns with design reinforcements, the failure function and the formula of the influence coefficient of reinforcement are obtained and expressed by multiple normalized design parameters with an analytical method. Based on the requirements on column reinforcement in codes, the variation laws of the influence coefficient of reinforcement are analyzed with multiple design parameters(e.g. load effect ratios) within common ranges. Considering the random properties of eccentricity and the prescribed probability models of horizontal earthquake action, vertical gravity load, concrete strength and steel strength, etc., the seismic capacity reliability is obtained for RC columns with tension failure by the Monte Carlo method. The results indicate that the variations of the influence coefficient of reinforcement are large for different combination cases of design parameters; the seismic capacity reliability is improved less with the increase of reinforcement for the columns with a smaller influence coefficient of reinforcement; the reliability is improved dramatically with the increase of reinforcement for the columns with a larger influence coefficient of reinforcement.