Caches are used to reduce the speed differential between the CPU and memory to improve the performance of modern processors. However, attackers can use contention-based cache timing attacks to steal sensitive information from victim processes through carefully designed cache eviction sets. And L1 data cache attacks are widely exploited and pose a significant privacy and confidentiality threat. Existing hardware-based countermeasures mainly focus on cache partitioning, randomization, and cache line flushing, which unfortunately either incur high overhead or can be circumvented by sophisticated attacks. In this paper, we propose a novel hardware-software co-design called BackCache with the idea of always achieving cache hits instead of cache misses to mitigate contention-based cache timing attacks on the L1 data cache. BackCache places the evicted cache lines from the L1 data cache into a fully-associative backup cache to hide the evictions. To improve the security of BackCache, we introduce a randomly used replacement policy (RURP) and a dynamic backup cache resizing mechanism. We also present a theoretical security analysis to demonstrate the effectiveness of BackCache. Our evaluation on the gem5 simulator shows that BackCache can degrade the performance by 1.33%, 7.34%, and 7.59% For OS kernel, single-thread, and multi-thread benchmarks.