Context. We present a study of the variability of the broad emission-line parameters of 3C390.3, an active galaxy with the doublepeaked emission-line profiles. We give a detailed analysis of the variation in the broad Hα and Hβ emission-line profiles, the ratios, and the Balmer decrement of different line segments. Aims. We explore the disk structure with an investigation of the variability of the broad-line profiles. This is assumed to emit the broad double-peaked Hβ and Hα emission lines in the spectrum of 3C390.3. Methods. We divided the observed spectra into two periods (before and after the outburst in 2002) and separately analyzed the variation in these two periods. First we analyzed the spectral emission-line profiles of the Hα and Hβ lines and measured the peak positions. Then, we divided the lines into several segments and measured the line-segment fluxes. The Balmer decrement variation for the entire Hα and Hβ fluxes and for the line segments was investigated and discussed. Additionally, we modeled the variations in the line parameters with an accretion disk model and compared our modeled line parameter variations with observed ones. Results. We compared the variability in the observed line parameters with the disk model predictions and found that the variation in line profiles and in the line segments corresponds to the emission of a disk-like broad-line region (BLR). But there is probably another additional emission component that contributes to the Hα and Hβ line center. We found that the variation in the line profiles is caused by the variation in the parameters of the disk-like BLR, first of all in the inner (outer) radius, which can well explain the line parameters variations in Period I. The Balmer decrement across the line profile has a bell-like shape and is affected not only by physical processes in the disk, but also by different emitting disk dimension of the Hα and Hβ line. Conclusions. The geometry of the BLR of 3C390.3 seems to be very complex, and inflows/outflows may be present, but evidently the broad-line region with its disk-like geometry is the dominant emitter.