Successful synthesis of the 124 high-T-c superconductor Y1-xCaxBa2Cu4O8 at ambient oxygen pressure is reported. A solid-state reaction technique using Cu(I)I instead of the conventional Cu(III)O in starting materials has been found to be effective for the normal oxygen-pressure synthesis of YBa2Cu4O8 as well as calcium-substituted Y1-xCaxBa2Cu4O8. It was found that careful attention must be paid in preparing high-quality Y1-xCaxBa2Cu4O8. The chemical state of the initial calcium compound was a critical factor in the successful synthesis of Y1-xCaxBaxCu4O8 at ambient oxygen pressure.