A comprehensive model atom was developed for Si I-II-III using the most up-to-date atomic data available so far. Based on non-local thermodynamic equilibrium (NLTE) line formation for Si I, Si II and Si III and high-resolution observed spectra, we determined the NLTE abundances for a sample of nine unevolved A9-B3 type stars with well-determined atmospheric parameters. For each star, NLTE reduces the line-to-line scatter for Si II substantially compared with the LTE case and leads to consistent mean abundances from lines of different ionization stages. In the hottest star of our sample, {iota} Her, Si II is subject to overionization that drives emission in the lines arising from the high-excitation doublet levels. Our NLTE calculations reproduced 10 emission lines of Si II observed in {iota} Her. The same overionization effect leads to greatly weakened Si II lines, which are observed in absorption in {iota} Her. Large positive NLTE abundance corrections (up to 0.98dex for 5055{AA}) were useful for achieving consistent mean abundances from lines of the two ionization stages, Si II and Si III. It was found that NLTE effects are overestimated for the Si II 6347, 6371{AA} doublet in {iota} Her, while the new model atom works well for cooler stars. At this stage, we failed to understand this problem. We computed a grid of the NLTE abundance corrections for lines of Si I, Si II and Si III in model atmospheres with effective temperatures and surface gravities characteristic of unevolved A-B type stars.