Concrete　structures　often　suffer　from　multiple　dynamic　loads,　or　prior　to　being　subjected　to　dynamic　loads　have　already　withstood　initial　loads.　The　mechanical　properties　of　concrete　materials　under　dynamic　loads　may　be　closely　linked　to　initial　loading　history　that　concrete　suffers.　This　paper　deals　with　the　investigation　of　the　effect　of　initial　static　load　and　initial　dynamic　load　on　dynamic　compressive　failure　of　concrete　materials　based　on　numerical　simulations.　A　meso-scale　modeling　method　was　established　and　a　total　of　147　three-dimensional　concrete　cubic　models　were　simulated.　It　is　demonstrated　in　research　results　that　the　strain　rate　effect　of　concrete　is　relatively　weak　under　low　strain　rates,　while　the　strain　rate　effect　is　significantly　enhanced　under　high　strain　rates.　Dynamic　compressive　strength　under　different　dynamic　loads　gradually　decreases　with　the　increasing　initial　static　load　and　the　increasing　strain　rate　can　weaken　the　influence　of　initial　static　load　on　dynamic　compressive　strength　of　concrete.　When　dynamic　load　changes　in　hardening　stage,　tangent　modulus　has　a　sudden　increase　and　compressive　stress　reaches　a　new　peak　strength.　A　sudden　increase　of　dynamic　load　in　softening　stage　reverses　the　postpeak　softening　to　postpeak　hardening　followed　by　a　second　peak　strength.　Initial　dynamic　load　plays　an　important　role　in　dynamic　compressive　failure　of　concrete,　especially　under　low　strain　rates.　The　numerical　results　compare　well　with　the　existing　test　results.