One of the necessary parameters needed for the interpretation of the light curves of transiting exoplanets or eclipsing binaries, as well as interferometric measurements of a star or microlensing events is how the intensity and polarization of a light change from the center to the limb. Scattering and absorption processes in stellar atmosphere affect both the center-to limb variation of intensity (CLVI) and polarization (CLVP). In this paper, we present a study of the CLVI and CLVP in continuum spectra considering different contributions of scattering and absorption opacity for different spectral type stars with spherical atmospheres. We solve the polarized radiative transfer equation in the presence of continuum scattering, considering spherical stellar model atmospheres. We developed two independent codes based on Feautrier and short characteristics methods to cross-check our results. We calculate the CLVI and CLVP in continuum for the Phoenix grid of spherical stellar model atmospheres for a range of $T_{eff} = 4000 - 7000 rm K$, $log g = 1.0 - 5.5$ and $lambda = 4000 - 7000 rm AA$, which are tabulated and available at the CDS. For sub-giant and dwarf stars ($log g = 3.0 - 4.5$), lower $log g$ and lower $T_{eff}$ of a star lead to higher limb polarization of the star. For giant and supergiant stars ($log g = 1.0 - 2.5$), the highest effective temperature yields the largest polarization. By decreasing of the $T_{eff}$ of a star down to $4500 - 5500 rm K$ (depending on $log g$) the limb polarization decreases and reaches a local minimum. It increases again down to $T_{eff}$ of $4000 rm K$. For the most compact dwarf stars ($log g = 5.0 - 5.5$) the limb polarization degree shows a maximum for models with $T_{eff}$ in the range $4200 - 4600 rm K$ (depending on $log g$) and decreases toward higher and lower temperatures.
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