Ultrasonic wavefield imaging (UWI) provides insightful spatial information about ultrasonic wave propagation in planar (2-D) space for nondestructive evaluation and structural health monitoring (NDE-SHM) applications. In all materials, the wavefronts of the incident and reflected waves propagate with unique patterns that may be represented by parametrized polar curves in 2-D geometric space. In this paper, a spatial ultrasonic wavefront characterization method based on a parametric curve laser scan is proposed to characterize the spatial ultrasonic wavefront for both isotropic and anisotropic materials. Three parametric curves (circular, hyperbolic, and cyclic-harmonic curves) were considered. Two wavefront characterization process were carried out, namely (i) deciding the parametric equation of the closed-form geometric plane curve via UWI, and (ii) measuring and updating the ultrasound via laser ultrasonic interrogation system (LUIS) and quantifying the values(s) of the predicted parametric curve equation using a temporal cross-correlation technique. The proposed method was tested on pristine aluminum and cross-ply CFRP plates to characterize the spatial incident and reflected wavefronts of the plates. The non-fiber direction region (105°⩽ϕS⩽165°) and the fiber direction region (165°⩽ϕS⩽195°) of the cross-ply CFRP plate were considered in the test. The laser circle scan and the laser cyclic-harmonic curve scan showed the ability to characterize the incident wavefronts of the S0 and A0 modes in the aluminum plate and the CFRP plate, respectively, followed by the laser hyperbolic curve scan. With the promising results obtained in the proposed method, the integration of the parametric curve scanning method into LUIS may provide a new approach to damage detection and useful information for ultrasonic algorithm design in NDE-SHM applications.