The present invention provides an oxide superconductor which has a relatively high transition temperature T.sub.c. This superconductor has the chemical formula (R.sub.1-x Ca.sub.x)(Ba.sub.1-y Sr.sub.y).sub.2 Cu.sub.3 O.sub.7-z wherein R is at least one rare earth element selected from the group consisting of Tm, Yb and Lu, x is with in the range of 0.1.ltoreq..times.0.5, y is within the range of 0.1.ltoreq. y .ltoreq.0.4 and z is within the range of 0.05 .ltoreq. z .ltoreq.(x/2+0.5). The invention further provides a method for producing the oxide superconductor which comprises firing a composition of the formula (R.sub.1-x Ca.sub.x)(Ba.sub.1-y Sr.sub.y).sub.2 Cu.sub.3 O.sub.7-z wherein R is at least one rare earth element selected from the group consisting of Tm, Yb and Lu, x is within the range of 0.1 .ltoreq..times..ltoreq.0.5 and y is within the range of 0.1 .ltoreq.y .ltoreq.0.4 at a temperature of from 750.degree. C. to the melting temperature of the composition under an oxygen partial pressure P(O.sub.2) of 0.001 atm .ltoreq.P(O.sub.2) .ltoreq.0.2 atm and then heat treating the composition to adjust the oxygen loss z to 0.05 .ltoreq.z .ltoreq.(x/2+0.5).