The rise of deep neural networks (DNNs) has driven an increased demand for computing power and memory. Modern DNNs exhibit high data volume variation (HDV) across tasks, which poses challenges for FPGA acceleration: conventional accelerators rely on fixed execution patterns (dataflow or sequential) that can lead to pipeline stalls or necessitate frequent off-chip memory accesses. To address these challenges, we introduce the Inter-Task Auto-Reconfigurable Accelerator (InTAR), a novel accelerator design methodology for HDV applications on FPGAs. InTAR combines the high computational efficiency of sequential execution with the reduced off-chip memory overhead of dataflow execution. It switches execution patterns automatically with a static schedule determined before circuit design based on resource constraints and problem sizes. Unlike previous reconfigurable accelerators, InTAR encodes reconfiguration schedules during circuit design, allowing model-specific optimizations that allocate only the necessary logic and interconnects. Thus, InTAR achieves a high clock frequency with fewer resources and low reconfiguration time. Furthermore, InTAR supports high-level tools such as HLS for fast design generation. We implement a set of multi-task HDV DNN kernels using InTAR. Compared with dataflow and sequential accelerators, InTAR exhibits $\mathbf{1.8\times}$ and $\mathbf{7.1 \times}$ speedups correspondingly. Moreover, we extend InTAR to GPT-2 medium as a more complex example, which is $\mathbf{3.65 \sim 39.14\times}$ faster and a $\mathbf{1.72 \sim 10.44\times}$ more DSP efficient than SoTA accelerators (Allo and DFX) on FPGAs. Additionally, this design demonstrates $\mathbf{1.66 \sim 7.17\times}$ better power efficiency than GPUs. Code: https://github.com/OswaldHe/InTAR