A new multi-frequency quasi-optical mode converter design for four frequency/mode pairs for a step-tunable gyrotron is discussed.The design frequency/mode pairs are 110 GHz/TE 22 ,6, 124.5 GHz/TE 24 ,7, 127.5 GHz/TE 2s ,7 and 107.5 GWTE 21 ,6. The design is for an 88 mm diameter variable-spacing double-disk vacuum window.which gives the radii values of roughly (Rl,x, Rl,z) = (6, 100) cm. Similarly, for mirror 2, (Rz,x' Rz,z) = (6.5,100) cm.The mirror design was done using a new method developed at the UW we call the Taylor-FFT algorithm [2]. The Gaussian beam is polarized in the xdirection and has a beam waist radius ofwo = 2.63 cm, located at the window plane (y = 25.4 cm), where the subscript"1" denotes mirror 1; the center of mirror 1 (offsets) is at (Xl,o'Yl,o,Zl,o) = (0.5, 5.7,18) cm; the tilt angles (Ol,x, 0l,z) are used to adjust the beam's center position to coincide with the center of mirror 2 and are usually set to 0 or very small values. The radii are estimated through paraxial Gaussian optics using the q-parameter, (2) 2 1 1 -----= --Superconducting Magnet