This talk will discuss concurrent functional regression models for batch data on Riemannian manifolds by estimating both mean structure and covariance structure simultaneously. The response variable is considered to follow a wrapped Gaussian process. Nonlinear relationship between manifold-valued response variables and multiple Euclidean covariates can be captured by this model in which the covariates could be either functional or scalar. Numerical results with both simulated data and real data will be presented to show the performance of the model.