The asymmetric (3 + 3) annulations of beta'-acetoxy allenoates with either 3-oxo-nitriles or pyrazolones have been realized by using 6'-deoxy-6'-[(L)-N,N-(2,2'-oxidiethyl)-valine amido]quinine (6h) as the catalyst. The three functions of catalyst 6h, including Lewis base (quinuclidine N), H-bond donor (amide NH), and Bronsted base (morpholine N), cooperatively take crucial roles on the chemo- and enantioselectivity, allowing for the construction of 4H-pyran and 4H-pyrano[2,3-c]pyrazole in high yields and enantioselectivity.