In 1904, Dickson [6] stated a very important conjecture. Now people call it Dickson’s conjecture. In 1958, Schinzel and Sierpinski [3] generalized Dickson’s conjecture to the higher order integral polynomial case. However, they did not generalize Dickson’s conjecture to the multivariable case. In 2006, Green and Tao [9] considered Dickson’s conjecture in the multivariable case and gave directly a generalized Hardy-Littlewood estimation. But, the precise Dickson’s conjecture in the multivariable case does not seem to have been formulated. In this paper, based on the idea in [8] a partial proof of Dickson's Conjecture is provided .