We calculate the anomalous dimensions of higher spin singlet currents in the critical O(N) vector model at order 1/N-2. The results are shown to be in agreement with the four-loop perturbative computation in phi(4) theory in 4-2 epsilon dimensions. It is known that the order 1/N anomalous dimensions of higher-spin currents happen to be the same in the Gross-Neveu and the critical vector model. On the contrary, the order 1/N-2 corrections are different. The results can also be interpreted as a prediction for the two-loop computation in the dual higher-spin gravity.