感謝桐丘的方法，可以實現排序。
冒泡排序方法實現數組排序，數組中元素為中文字符串，方法如下：

//數組排序
- (void)sortedArrayWithChineseObject:(NSMutableArray *)mArray { 
    for(NSUInteger i = 0; i < mArray.count - 1; i++) { 
      for(NSUInteger j = 0; j < mArray.count - i - 1; j++) { 
          NSString *pinyinFirst = [NSString lowercaseSpellingWithChineseCharacters:mArray[j]]; 
          NSString *pinyinSecond = [NSString lowercaseSpellingWithChineseCharacters:mArray[j + 1]]; 
          //此處為升序排序，若要降序排序，把NSOrderedDescending 換為NSOrderedAscending即可。   
          if(NSOrderedDescending == [pinyinFirst compare:pinyinSecond]) { 
              NSString *tempString = mArray[j]; 
              mArray[j] = mArray[j + 1]; 
              mArray[j + 1] = tempString; 
            } 
         } 
      } 
  //測試
  // NSLog(@"%@", mArray);
}

漢字轉拼音，NSString的分類
NSString+ChineseCharactersToSpelling.h

#import <Foundation/Foundation.h>

@interface NSString (ChineseCharactersToSpelling)

+(NSString *)lowercaseSpellingWithChineseCharacters:(NSString *)chinese;

@end

NSString+ChineseCharactersToSpelling.m

#import "NSString+ChineseCharactersToSpelling.h"

@implementation NSString (ChineseCharactersToSpelling)

+(NSString *)lowercaseSpellingWithChineseCharacters:(NSString *)chinese {
    //轉成了可變字符串
    NSMutableString *str = [NSMutableString stringWithString:chinese];
    //先轉換為帶聲調的拼音
    CFStringTransform((CFMutableStringRef)str, NULL, kCFStringTransformMandarinLatin, NO);
    //再轉換為不帶聲調的拼音
    CFStringTransform((CFMutableStringRef)str, NULL, kCFStringTransformStripDiacritics, NO);
    //返回小寫拼音
    return [str lowercaseString];
}

@end