The invention provides a production method of tissue paper or kitchen paper, and a paper preparation method thereof. The production method comprises the steps of primary drying, wet wrinkling and paper picking, secondary drying and rolling. The paper is prepared from 20 parts of needle-leaved fibers, 35 parts of bamboo fiber, 25 parts of bagasse fibers, 0.25wt% of a softener, 1.25wt% of a wet strength agent, 10.8wt% of a kenaf core mixture and 3.6% of immobilized compound lipase; and paper is wrinkled through wet wrinkling in combination with a vacuum paper pickup device, so that the quality of the paper is guaranteed, and the problem of paper scraps is solved. The modified kenaf core and the immobilized compound lipase are added into the paper, the optimal addition amounts are obtained through studying, the grease adsorption performance of the paper is improved through addition of kenaf core, wet wrinkling and vacuum paper picking operation can be further guaranteed, and the finishedproduct quality of the paper is guaranteed.