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In this paper, we explore how to estimate the phase damping parameterγ and the tunneling amplitude parameter?from a spin-boson dephasing quantum model by periodical projective measurements. The preparation of initial states is accomplished by performing the period measurements in our scheme. The parameter γ can be always estimated when projective measurement bases are chosen as θ =π/2 and φ =0. Based on the estimated value of γ and the interval information of?, we can select another measurement bases (θ=π/4 andφ=π/2) to obtain the estimated value of?. A coherent control is indispensable to estimate? ifγ is in the interval of?;whereas the control is not necessary ifγ is out of the known interval of?. We establish the relation between the optimal period time and the parameterγor? in terms of Fisher information. Although the optimal measurement period cannot be selected beforehand, the aforementioned relation can be utilized to adjust the measurement period to approach the optimal one.