Diffusion magnetic resonance imaging (dMRI), as a powerful non-invasive white matter imaging technology, plays an important role in studying brain white matter. The fiber orientation distribution functions (fODFs) derived from dMRI data provide the key directional information of fiber tracts for revealing the 3D geometric structure of brain white matter. The estimation of fODFs faces two challenges, including (i) the demand for dMRI data densely sampled in q-space and (ii) the joint consideration of x-q space. To address these challenges, we propose a mixture learning framework with q-space sparely sampled dMRI data as input. Specifically, we propose an x-space learning module based on 3D U-Net to learn x-space features and a q-space learning module based on spherical convolutional neural networks to learn q-space features. Two kinds of features are then fused with a mixture learning fusion module for fODFs estimation. The whole framework is supervised with an x-q space loss function. Our framework makes full use of joint x-q space information for fODFs estimation with clinically available q-space sparsely sampled dMRI data. Extensive experiments on three public datasets show that our framework is effective in fODFs estimation and outperforms cutting-edge models.