High mechanical advantage as well as low and steady slide speed within the working stroke Sn are the fundamental requirements for the working mechanism of servo-mechanical press. Currently, the Crank-Triangular Linkage-Elbow (CTLE) mechanism has attracted more and more attention from researchers and manufacturers of servo presses. This paper presents a new analysis and design method of CTLE. The mechanism is decomposed into two sub-units: crank and triangular-linkage elbow, followed by the kinematic and force analysis of each sub-unit. The influences of each structural parameter on the working performance are obtained and can be used as the basis for preliminary design. Through the offset design, the mechanical advantage peaks of the two units, MA1max and MA2max, do not occur at the same time: MA1max is located near Sn, while MA2max is just at BDC (Bottom Dead Center). Because the mechanical advantage of the whole mechanism is the product of the two subunits, the designed mechanism can obtain high and steady mechanical advantage together with low and steady slide speed within Sn. After preliminary design, the scheme can be further modified by numerical simulation and optimization. Hence the design efficiency can be improved.