In this paper, a novel SPH (Smoothed Particle Hydrodynamics)-based implicit structure model as well as its refined coupled fully-Lagrangian meshfree FSI (Fluid-Structure Interaction) solver are presented. The implicit structure model is founded through consideration of conservation law of linear momentum. The implicit time integration is achieved along with the assumption of linear elastic material. For development of refined implicit structure model, three novel schemes are considered; (1) High-order implicit Time integration (HT) scheme is considered for enhanced implicit update of particles’ velocities and positions; (2) Predictor-Corrector (PC) method is incorporated for improved estimation of rotation matrix; (3) High-order Discretization (HD) operator is employed for consistent calculation of deformation gradient and acceleration by elastic force. The proposed SPH-based implicit structure model is coupled with a refined ISPH fluid model so as to develop an enhanced fully-Lagrangian meshfree FSI solver, where consistent time coupling between incompressible fluid flow and stiff structures can be achieved by using the same time step sizes in both phases. The proposed implicit structure model as well as its corresponding FSI solver are verified in terms of robustness and accuracy by reproducing a set of well-known benchmark tests.