This article presents a combined Bahl-Cocke-Jelinek-Raviv (BCJR) and deep neural network (DNN) turbo-detection architecture for 1-D hard disk drive (HDD) magnetic recording. Simulated HDD readings based on a grain flipping probabilistic (GFP) model are input to a linear filter equalizer with a 1-D partial response (PR) target. The equalizer output is provided to the BCJR detector in order to minimize the intersymbol interference (ISI) due to the PR mask. The BCJR detector's log-likelihood-ratio (LLR) outputs (along with the linear equalizer outputs) are then input to the DNN detector, which estimates the signal-dependent media noise. The media noise estimate is then fed back to the BCJR detector in an iterative manner. Several DNN media noise estimation architectures based on fully connected (FC) and convolutional neural networks (CNNs) are investigated. For GFP data at 48 nm track pitch and 11 nm bit length, the CNN-based BCJR-DNN turbo detector reduces the detector bit error rate (BER) by 0.334× and the per bit computational time by 0.731× compared to a BCJR detector that incorporates 1-D pattern-dependent noise prediction (PDNP). The proposed BCJR-DNN turbo detection architecture can be generalized for two-dimensional magnetic recording (TDMR).