Convective-core overshoot mixing is a significant uncertainty in stellar evolution. Because numerical simulations and turbulent convection models predict exponentially decreasing radial rms turbulent velocity, a popular treatment for overshoot mixing is to apply a diffusion process with an exponentially decreasing diffusion coefficient. It is important to investigate the parameters of the diffusion coefficient because they determine the efficiency of the mixing in the overshoot region. In this paper, we have investigated the effects of the core overshoot mixing on the properties of the core in solar models. We have constrained the parameters of the overshoot model by using helioseismic inferences and the observation of the solar B-8 neutrino flux. For solar-mass stars, the core overshoot mixing helps to prolong the lifetime of the convective core developed at the zero-age main sequence. If the strength of the mixing is sufficiently high, then the convective core in a solar model could survive until the present solar age, leading to large deviations of the sound speed and density profiles compared with the helioseismic inferences. The B-8 neutrino flux also favours a radiative solar core. These observations provide a constraint on the parameters of the exponential diffusion model of the convective overshoot mixing. A limited asteroseismic investigation of 13 Kepler low-mass stars with 1.0 < M/M-circle dot < 1.5 shows a mass-dependent range of the overshoot parameter. The overshoot mixing processes for different elements are analysed in detail. It is found that the exponential diffusion overshoot model leads to different effective overshoot mixing lengths for elements with different nuclear equilibrium time-scales.