In this paper, a penalty difference finite element (PDFE) method is presented for the 3D Stokes equations by using the FE pair $({\bf P}{1,1},P{0,1})$. This new method consists of transmitting the FE solution of the 3D Stokes equations in the direction $(x,y,z)$ into a series of the FE solution pair $(w_h^k,p_h^{k})$ based on the FE space pair $W_h\times M_h$ of the 2D penalty Stokes equations and the FE solution $u_{3h}^k$ based on the FE space $S_h\cap H^10(\o)$ of the elliptic equation, where $u_h=\sum^{l_3-1}{k=1}u_h^k\phi_k(z)$ and $p_h=\sum^{l_3}{k=1}p_h^{k}\psi_k(z)$ with $u_h^k=(w_h^k,u{3h}^k)^{\top}$ and $w_h^k=(u_{1h}^k,u_{2h}^k)$ and $\phi_k(z)$ is $P_1$-nodal point basis functions related to point $z_k$ and $\psi_k(z)$ is $P_0$-piecewise constant basis functions related to element $(z_{k-1},z_k)$ in the direction $z$. Here, the finite element space pair $W_h\times M_h$ is only required to satisfy the inf-sup condition.