The long-term evolution of a circumstellar disk starting from its formation and ending in the T Tauri phase was simulated numerically with the purpose of studying the evolution of dust in the disk with distinct values of viscous alpha-parameter and dust fragmentation velocity v_frag. We solved numerical hydrodynamics equations in the thin-disk limit, which are modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a maximum radius a_r. The former is strictly coupled to the gas, while the latter interacts with the gas via friction. The conversion of small to grown dust, dust growth, and dust self-gravity are also considered. We found that the process of dust growth known for the older protoplanetary phase also holds for the embedded phase of disk evolution. The dust growth efficiency depends on the radial distance from the star - a_r is largest in the inner disk and gradually declines with radial distance. In the inner disk, a_r is limited by the dust fragmentation barrier. The process of small-to-grown dust conversion is very fast once the disk is formed. The total mass of grown dust in the disk (beyond 1 AU) reaches tens or even hundreds of Earth masses already in the embedded phase of star formation and even a greater amount of grown dust drifts in the inner, unresolved 1 AU of the disk. Dust does not usually grow to radii greater than a few cm. A notable exception are models with alpha <= 10^{-3}, in which case a zone with reduced mass transport develops in the inner disk and dust can grow to meter-sized boulders in the inner 10 AU. Grown dust drifts inward and accumulates in the inner disk regions. This effect is most pronounced in the alpha <= 10^{-3} models where several hundreds of Earth masses can be accumulated in a narrow region of several AU from the star by the end of embedded phase. (abridged).
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