Using a dissipative particle dynamics approach, we study the conformations and interactions of a cylindrical polyelectrolyte brush (CPB) with added salt. The effects of counterion valency on the conformational behaviors of the CPB are analyzed in detail by considering various parameters like the distribution of bond lengths, the mean distance between two grafting points, the order parameter of side chains, etc. The lyotropic behavior of the CPB is also investigated through examining the backbone persistence. Our simulations demonstrate that the presence of the multivalent counterions can induce the collapse of the CPB, leading to various conformations. We identify a horseshoe to helical to coil-like conformation transition with increasing counterion valency. An important factor for the collapse of the CPB is the fact that the strong condensation of counterions induced by the higher electrostatic correlations decreases the osmotic pressure inside the brush. It is found that the ratio of the backbone persistence to the diameter of the CPB, l(p)/d, can only be affected to a slight extent by changing the counter-ion valency and the side chain length. These results may provide a valuable guideline that can be used to tailor the microstructure of the systems and to yield desired macroscopic behaviors.