With the advancement of machine learning, domain adaptation has become increasingly important. Traditional research in domain adaptation has primarily focused on Unsupervised Domain Adaptation (UDA) and Semi-Supervised Domain Adaptation (SSDA). However, in many practical applications, it is common to encounter scenarios where both domains have labeled and unlabeled samples, which complicates the handling of domain adaptation. The scarcity of solutions to these scenarios further underscores the necessity of developing new methods to effectively explore the labeled and unlabeled samples. This paper proposes the problem of Bi-directional Semi-Supervised Domain Adaptation (BiSSDA) and a method of Gradient discrepancy minimization and labeled Class Centroid Align (GCCA) to address this problem. In GCCA, labeled and unlabeled samples from both domains are passed through a generator G and two classifiers F_1 and F_2, the generator G opposes with F_1 and F_2 during training and in which both domains are better aligned via gradient and class centroid alignment. Extensive experiments on three widely used datasets demonstrate that GCCA significantly outperforms CGDM and several previous SSDA methods in terms of exploring the labeled and unlabeled samples in both domains and significantly reduce the reliance on labeled data in bi-directional domain adaptation through cooperation between two domains. The code of the proposed method is available at the website of gitee.com/ymw12345/gcca.