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Due to the complexity of wind speed, it has been reported that mixed-noise models, constituted by multiple noise distributions, perform better than single-noise models. However, most existing regression models suppose that the noise distribution is single. Therefore, we study the Least square <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>V</mi> <mi>R</mi> </mrow> </semantics> </math> </inline-formula> of the Gaussian–Laplacian mixed homoscedastic (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mi>L</mi> <mi>M</mi> <mo>−</mo> <mi>L</mi> <mi>S</mi> <mi>S</mi> <mi>V</mi> <mi>R</mi> </mrow> </semantics> </math> </inline-formula>) and heteroscedastic noise (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mi>L</mi> <mi>M</mi> <mi>H</mi> <mo>−</mo> <mi>L</mi> <mi>S</mi> <mi>S</mi> <mi>V</mi> <mi>R</mi> </mrow> </semantics> </math> </inline-formula>) for complicated or unknown noise distributions. The ALM technique is used to solve model <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mi>L</mi> <mi>M</mi> <mo>−</mo> <mi>L</mi> <mi>S</mi> <mi>S</mi> <mi>V</mi> <mi>R</mi> </mrow> </semantics> </math> </inline-formula>. <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mi>L</mi> <mi>M</mi> <mo>−</mo> <mi>L</mi> <mi>S</mi> <mi>S</mi> <mi>V</mi> <mi>R</mi> </mrow> </semantics> </math> </inline-formula> is used to predict short-term wind speed with historical data. The prediction results indicate that the presented model is superior to the single-noise model, and has fine performance.