Evaluating the impact of different meteorological conditions on apple yield and predicting the future yield in Yantai City is essential for production. Furthermore, it provides a scientific basis for the increase in apple yield. In this study, first, a grey relational analysis (GRA) was used to determine the quantitative relationship between different meteorological factors and meteorological yield which is defined as affected only by meteorological conditions. Then, the comprehensive meteorological factors extracted by a principal component analysis (PCA) were used as inputs for multiple linear regression (MLR). The apple yield accuracy was compared with the lasso regression prediction. Trend analysis showed that the actual apple yield increased annually, but the meteorological yield decreased annually over a long time. Correlation ranking illustrated that the meteorological yield was significantly correlated with the frost-free period, the annual mean temperature, the accumulated temperature above 10 °C, etc. The good consistency between GRA and MLR–PCA showed that the accumulated temperature above 10 °C, the March–October mean temperature, and the June–August mean temperature are key meteorological factors. In addition, it was found that the principal components F2, F4, and F5 were negatively correlated with meteorological yield, while the principal components F1 and F3 were positively correlated with meteorological yield. Moreover, the MLR–PCA model predicted the apple yield in 2020 as 47.256 t·ha−1 with a 7.089% relative error. This work demonstrates that the principal component regression model can effectively extract information about different meteorological factors and improve the model’s accuracy for analyzing key meteorological factors and predicting apple yield.