A Lamb wave in a plate with a finite width has both thickness and width modes, whereas only thickness modes exist in an infinitely wide plate. The thickness and width modes are numerously formed in a finite-width plate, and they all have different cut-off frequencies, wave velocities, and wave structures. These different characteristics can be utilized in various applications, but a selective generation method for a particular Lamb wave mode in a finite-width plate has not been sufficiently studied, and only a method using multiple elements has been reported. This paper presents the selective generation of a certain Lamb wave mode in a finite-width plate by an angle-beam excitation method using single or dual wedges. In the proposed generation method, a specially designed wedge with grooves or a patch having insulation layers is employed for partial acoustic insulation of the ultrasonic energy incident into the plate. The feasibility of the proposed method was investigated through finite element method (FEM) simulations for Lamb wave excitation and propagation, and then experimentally demonstrated by the measurement of Lamb wave propagation using a laser scanning vibrometer.