(1) Background: Neoadjuvant therapy is the main therapeutic strategy for human epidermal growth factor receptor 2 (HER2)-positive breast cancer patients, and the combination of trastuzumab and pertuzumab (HP) has become a routine treatment. How to predict and screen patients who are less likely to respond to neoadjuvant therapy is the focus of research. The androgen receptor (AR) is a biomarker that is widely expressed in all breast cancer subtypes and is probably related to treatment response and prognosis. In this study, we investigated the relationship between AR expression and treatment response in HER2-positive breast cancer patients treated with HP neoadjuvant therapy. (2) Methods: We evaluated early breast cancer patients treated with HP neoadjuvant therapy from Jan. 2019 to Oct. 2020 at Peking University First Hospital Breast Cancer Center. The inclusion criteria were as follows: early HER2-positive breast cancer patients diagnosed by core needle biopsy who underwent both HP neoadjuvant therapy and surgery. We compared the clinical and pathological features between pathological complete response (pCR) and non-pCR patients. (3) Results: We included 44 patients. A total of 90.9% of patients received neoadjuvant therapy of taxanes, carboplatin, trastuzumab and pertuzumab (TCHP), and the total pCR rate was 50%. pCR was negatively related to estrogen receptor (ER) positivity (OR 0.075 [95% confidence interval (CI) 0.008–0.678], p = 0.021) and positively related to high expression levels of AR (OR 33.145 [95% CI 2.803–391.900], p = 0.005). We drew a receiver operating characteristic (ROC) curve to assess the predictive value of AR expression for pCR, and the area under the curve was 0.737 (95% CI 0.585–0.889, p = 0.007). The optimal cutoff of AR for predicting pCR was 85%. (4) Conclusion: AR is a potential marker for the prediction of pCR in HER2-positive breast cancer patients treated with HP neoadjuvant therapy.