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This work investigates a metasurface design to achieve remarkable second harmonic generation (SHG) conversion efficiency and enhance effective nonlinear susceptibility using the finite element method. The elements of the designed structure are composed of a rectangular split-ring resonator Ag film, a bowtie-shaped Ag nanoantenna, and a pair of Bi bars that induce nonlinear optical phenomena due to the nonuniform distribution of the electric and magnetic fields within the device surface. The simulation results agree perfectly with the theory and demonstrate outstanding achievements in terms of SHG conversion efficiency (<i>η</i>) and effective nonlinear susceptibility (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced open="|" close="|" separators="|"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></mrow></mfenced></mrow></semantics></math></inline-formula>). Specifically, the metasurface reaches a peak <i>η</i> value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.544</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup></mrow></semantics></math></inline-formula> and an effective nonlinear susceptibility of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.4</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>4</mn></mrow></msup></mrow></semantics></math></inline-formula> pm/V. This work presents a novel and versatile design to achieve high <i>η</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced open="|" close="|" separators="|"><mrow><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></mrow></mfenced><mo> </mo></mrow></semantics></math></inline-formula>in an SHG metasurface.