We study the low-energy electronic structure of three-dimensional Dirac semimetal, Cd3(As1-xPx)2 [x=0 and 0.34(3)], by employing angle-resolved photoemission spectroscopy (ARPES). We observe that the bulk Dirac states in Cd3(As0.66P0.34)2 are gapped out with an energy of 0.23 eV, contrary to the parent Cd3As2 in which the gapless Dirac states have been observed. Thus, our results confirm the earlier predicted topological phase transition in Cd3As2 with perturbation. We further notice that the critical P substitution concentration, at which the two Dirac points that are spread along the c-axis in Cd3As2 form a single Dirac point at Γ, is much lower [xc(P)<0.34(3)] than the predicted value of xc(P)=0.9. Therefore, our results suggest that the nontrivial band topology of Cd3As2 is remarkably sensitive to the P substitution and can only survive over a narrow substitution range, i.e., 0≤x(P)<0.34(3).