Brain-wide and genome-wide association (BW-GWA) study is presented in this paper to identify the associations between the brain imaging phenotypes (i.e., regional volumetric measures) and the genetic variants [i.e., single nucleotide polymorphism (SNP)] in Alzheimer's disease (AD). The main challenges of this study include the data heterogeneity, complex phenotype-genotype associations, high-dimensional data (e.g., thousands of SNPs), and the existence of phenotype outliers. Previous BW-GWA studies, while addressing some of these challenges, did not consider the diagnostic label information in their formulations, thus limiting their clinical applicability. To address these issues, we present a novel joint projection and sparse regression model to discover the associations between the phenotypes and genotypes. Specifically, to alleviate the negative influence of data heterogeneity, we first map the genotypes into an intermediate imaging-phenotype-like space. Then, to better reveal the complex phenotype-genotype associations, we project both the mapped genotypes and the original imaging phenotypes into a diagnostic-label-guided joint feature space, where the intraclass projected points are constrained to be close to each other. In addition, we use l-norm minimization on both the regression loss function and the transformation coefficient matrices, to reduce the effect of phenotype outliers and also to encourage sparse feature selections of both the genotypes and phenotypes. We evaluate our method using AD neuroimaging initiative dataset, and the results show that our proposed method outperforms several state-of-the-art methods in term of the average root-mean-square error of genome-to-phenotype predictions. Besides, the associated SNPs and brain regions identified in this study have also been shown in the previous AD-related studies, thus verifying the effectiveness and potential of our proposed method in AD pathogenesis study.