Recently, a new strain smoothing method, named as the strain-smoothed element (SSE) method, is developed for analysis of two- and three-dimensional solid and shell structures. The SSE method does not require any special domains for strain smoothing, and no additional degree of freedom is needed for solution improvement. In this paper, we present the formulation of the 3-node triangular finite element adopting the SSE method. The strain-smoothed element passes the basic tests (patch, isotropy and zero energy mode tests), and shows improved convergence behaviors in various numerical examples.