Extenics, a new theory for study of contradictory problems in the realistic world is a crossing subject among mathematics subject, and system subject and thoughts subject.Its theoretical pillars are the theory of matter-element and the theory of extension set.Based on matter-element and extension set, contradictory problems can be transformed compatible problems by matter-elements transformation.A concept of matter-element matrix with the same characteristics is introduced, and the concept of level variable characteristic value of extension assessment method is suggested.The method for determination of extension weights by simple dependent function is proposed.The problem of map quality evaluation is a complicated problem because it contains certain factors and uncertain factors.In fact, the problem of map quality evaluation is a non-compatible problem.The former evaluation method did not resolve this problem.On these bases, the extension assessment method is firstly used to evaluate map quality.A new extension synthesis model has been discussed in this paper.Moreover, the flowchart of the extension evaluation method is developed.The basic idea of this method is shown as following:In order to describe the non-compatibility among the indexes of map evaluation and the results of single indexes, the matter-element transformation was used for transforming the non-compatible problem into compatible problem.The classification of object is described by the value of the correlation function of extension set.So the qualitative evaluation can expand to quantitative evaluation.On the basis of designing the classical matter-element matrixes of each evaluation class, extensional matter-element matrix include all evaluation classes, calculating the correlation degrees between the standard to be evaluated and each evaluation class.The coincidences of standard to be evaluated with each evaluation classes were evaluated and the comprehensive evaluation was made further according the quantities of correlation degrees.The concrete steps of synthesize evaluation are as follows:Firstly, in order to construct the condition set, select the evaluation indexes and design the classification criterion of map quality.Second, with a view to calculate the correlation value of sample with practical data, establish the correlation function and weight function.Finally, in accordance with the calculated value, the category is selected.At the same time a practical example is introduced.In this example, the general error and failure report, great normal error and failure report, technique modification, mathematical precision, line print quality, sign quality and annotate quality, groom quality, legend factor are selected as evaluation indexes.And the grade of map quality is divided into 6 kinds of class, excellent, above good, good, under good, normal, and under standard.The comprehensive appraisement is made for map quality evaluation using the extension method and other evaluation methods.Results form the extension method is good.Moreover, compared with the other methods, it has shown that this method is feasible to assess map qualities, which is objectively reasonable and widely applicable.And the authors believe that the application of the extension theory to map quality evaluation has profound practical prospect because the extenics has profound practical background.