In this paper, we study the influence of the parameters for the accelerating Kerr-Newman black hole on the shadows and the constraints, extensively. We find that the rotating parameter a, the charge parameter e, and the inclination angle ${\theta }_0$ affect the shadow qualitatively similar to that of Kerr-Newman black holes. The result shows that the size of the shadow will scale down with the accelerating factor A. Besides, the factor A also can affect the best viewing angles, which make the observations maximum deviate from ${\theta }_0=\frac{\pi }{2}$, and the degree of the deviations are less than 1%. Then, we assume the M87* as an accelerating Kerr-Newman black hole with the mass $M=6.5\times {10}^9{M}_{\odot }$ and the distance $r_0=16.8Mpc$. Combining the EHT observations, we find that neither the observations, circularity deviation ΔC or axial ratio $D_x$ can distinguish the accelerating black hole or not. However, the characteristic areal-radius of the shadow curve $R_a$ can give corresponding constraints on the parameters of the accelerating Kerr-Newman black hole. The result shows that the bigger accelerating factor A is, the stronger constraints on the rotating parameter a and charged parameter e. The maximum range of the accelerating factor is $A{r}_0\le 0.558$ for a accelerating Schwarzschild case with $(a/M=e/M=0)$, and for an extremely slow accelerating case $(A{r}_0\le 0.01)$, the ranges of rotating parameter a and charged parameter e are $a/M\in (0,1)$ and $e/M\in (0,0.9)$.