Based on the reproducing kernel theory, we solve the nonlinear fourth order boundary value problem in the reproducing kernel space $W_2^5[0,1]$. Its approximate solution is obtained by truncating the n-term of the exact solution and using the $\epsilon$-best approximate method. Meanwhile, the approximate solution $u_n^{(i)}(x)$ converges uniformly to the exact solution $u^{(i)}(x),(i,0,1,2,3,4)$. The validity and accuracy of this method are verified by some examples.