Photoproduction of J/psi, is considered including the color-octet contributions from the various partial wave states, (2S+1)L(J) = S-1(0), S-3(1), and P-3(J). The production cross section depends on three new nonperturbative parameters defined in NRQCD, called the color-octet matrix elements. Using the color-octet matrix elements determined by fitting the J/psi production at the Fermilab Tevatron, we find that the color-octet (<c(c)over bar>)(8)(S-1(0) and P-3(J)) contributions to the J/psi, photoproduction at the fixed target experiments and at DESY HERA are too large compared to the data on sigma(gamma+p-->J/psi+X) in the forward direction, and the z distribution of J/psi. The P-T(2) distribution of J/psi and the total inelastic J/psi, production rate as a function of root s(gamma p) are predicted including color-octet contributions. We also briefly digress on the B-->J/psi+X and observe the similar situation. This may be an indication that the color-octet matrix elements determined from the J/psi, production at the Tevatron, especially [0\O-8(psi)(S-1(0))\0] and [0\O-8(psi)(P-3(J))\0], might have been overestimated by an order of magnitude.