How to defend supreme authority of constitution and finish making constitution judicative is a new problem which belongs to building socialism political civilization at present.

Constitution supremacy is the product of the right civilization and the primary symbol of the law civilization.

Inspecting the present state of constitution authority of China, the paper points out the existence of superior policy and superior law in reality, which makes our constitution only have formal authority, but the essential authority does not exist.

Thus,in order to uphold constitution authority,the nation-wide constitution awareness must be developed.

The judicial application of the constitution helps to establish the authority of the constitution and to build a real country under the rule of law.

Constitutional authority s formation rests on the switch from authoritarianism to democracy, meanwhile, the construction of democracy also depends on the formation of constitutional authority.

Governing a country by law is first of all to govern a country by the constitution and maintain the constitutional authority, which requires to greatly develop socialist market economy, further enhance the construction of democratic politics.

With the help of due process, we can gain constitutional authority from the constitutional belief, majesty and supremacy.

To establish real authority,the institutional authority of constitution should be clanged into the realistic one, which relies more on the constitutional consciousness of the subject,in whose mind the belief of anthority should be built up.