For $0\leα<1$ and a uniform hypergraph $G$, the $α$-spectral radius of $G$ is the largest $H$-eigenvalue of $α\mathcal{D}(G) +(1-α)\mathcal{A}(G)$, where $\mathcal{D}(G)$ and $\mathcal{A}(G)$ are the diagonal tensor of degrees and the adjacency tensor of $G$, respectively. We give upper bounds for the $α$-spectral radius of a uniform hypergraph, propose some transformations that increase the $α$-spectral radius, and determine the unique hypergraphs with maximum $α$-spectral radius in some classes of uniform hypergraphs.