The present study aims to assess strengths and impact resistance of functionally graded concrete (FGC) incorporating recycled concrete aggregate (RCA) and polypropylene (PP) fiber to fabricate an environmentally friendly construction material towards sustainability for concrete industry. For this purpose, four concrete mixture proportions were designed, including normal concrete with 100% crushed stone (NC), normal concrete with 0.3% PP fiber (PNC), recycled aggregate concrete with 50% crushed stone replacement by RCA (RAC), and RAC with 0.3% PP fiber (PRAC). Four types of two-layered FGC specimens including NC-NC, NC-PNC, RAC-RAC, and RAC-PRAC were employed to investigate mechanical strengths and impact resistance at designated ages. Results showed that all the FGC specimens had the compressive and flexural strengths at 28 days corresponding to above 50 MPa and 5 MPa, respectively. The FGC containing RCA (RAC-RAC, and RAC-PRAC) had the inferior strengths and impact resistance than that with 100% crushed stone (NC-NC and NC-PNC), regardless of curing age. The FGC with the bottom layer reinforced by PP fiber (NC-PNC and RAC-PRAC) had the higher flexural strength (3.0–5.8%) and impact resistance (9.4–24.6%) at 28 days than that without PP fiber (NC-NC and RAC-RAC) while their compressive strengths had nearly the same, regardless of the RCA replacement. The positive relationships between strengths and impact resistance were established. In conclusion, the FGC with 50% RCA replacement and 0.3% PP fiber in the bottom layer in the present study could be suggested for sustainable structural applications against high external loadings.