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The main purpose of this paper is to study the global existence and uniqueness of solutions for three-dimensional incompressible magnetic induction equations with Hall effect provided that <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mo stretchy="false">∥</mo><msub><mi>u</mi><mn>0</mn></msub><mo stretchy="false">∥</mo></mrow><mrow><msup><mi>H</mi><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo><mi>ε</mi></mrow></msup></mrow></msub><mo>+</mo><msub><mrow><mo stretchy="false">∥</mo><msub><mi>b</mi><mn>0</mn></msub><mo stretchy="false">∥</mo></mrow><msup><mi>H</mi><mn>2</mn></msup></msub></mrow></semantics></math></inline-formula><inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo><</mo><mi>ε</mi><mo><</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> is sufficiently small. Moreover, using the Fourier splitting method and the properties of decay character <inline-formula><math display="inline"><semantics><msup><mi>r</mi><mo>*</mo></msup></semantics></math></inline-formula>, one also shows the algebraic decay rate of a higher order derivative of solutions to magnetic induction equations with the Hall effect.